As far as I know we simply will not have any particular reason to give to that.

Now, hillsonghoods mentions two good points in his post when an answer was removed: (a) there's not one canon (b) the process by which we end up with certain texts needs to be discussed. And he helpfully points out a passage in which a Biblical text does mention Alexander the Great. I will largely focus on the second point I mention, but not in a definitive way. Rather, that point got me thinking about the difficulties that seem to come with the question (especially as I tried to find research I had access to that might offer more helpful answers and I continually came up with nothing)

I'll preface my quick response with a quick note: I suggest crossposting this /r/AskBibleScholars since there are some people who will know a lot about this topic. But I will also quickly add that the text we have already had mentioned is from 1 Maccabees, a text which does not appear in the Protestant Bible but does appear in Orthodox and Catholic Bibles. The process by which the canon had some alterations (namely, Protestants viewed some texts as less-inspired or not-inspired and removed them from their canon and, overtime, largely stopped reading them) is, I think, what hillsonghoods was getting at.

Another thing to consider is that 1 Macacabees is one might call an intertestamental book -- meaning it was composed sometime between the Old Testament and the New Testament (though it would be considered part of the Old Testament in some traditions). This is relevant because 1 Maccabees is a later text (written about the time after Alexander the Great had died, in particular). I suspect OP's question is concerned with why contemporary texts in the Bible don't mention him. A quick look at the common dating of books suggests that the texts which were written around Alexander's reign are Chronicles (dealing with the history of the North and South kingdoms), a smattering of wisdoms texts (Job, Ecclesiastes), and sections of Psalms. And perhaps Ezra and Nehemiah were starting to take shape. If you were to ask me what texts I would expect to speak about such a figure, I would say "history or prophetic texts" but the texts that are commonly thought to originate from that time all pretty insular in focus (history of the people and a record of the restoration of the people in the land). If common dating of texts is correct, the question is really why weren't more prophetic texts being composed or preserved during this time?

Bradley Gregory, in "Historical Candidates for the fallen King in Sirach 10,10" (from Zeitschrift Für Die Alttestamentliche Wissenschaft 126, no. 4 (2014): 589-591) believes that Sirach 10:10 ("A long illness baffles the physician; the king of today will die tomorrow," New Revised Standard Version) is a reference to Alexander the Great and writes:

The significance of Alexander’s fatal illness for Jews living much later is confirmed by the brief account of Alexander the Great in 1 Maccabees in which the author’s main point about Alexander is that his illness, described as »falling on his bed«, was a reversal of his arrogance, described as having a heart that was »exalted and lifted up« (p. 591)

Gregory's article is sadly short (he's mostly just suggesting a possible figure to consider), but he believes that in the original languages there's also commonality between the Sirach passage and 1 Maccabees. Yet I believe Gregory's potential solution to a minor quandary (does 10:10 refer to a specific monarch?) raised another question: if Alexander's perceived arrogance was so well-known that this would have been seen as a clear reference to him, why do we not have more Jewish literature concerning him? To which there is no clear answer. I tried to do a search to see if there are non-biblical, religious texts from the Jewish people that mention him but that's outside of my realm of expertise.

And I'm not sure there will be answers on this question that do not go into speculation. Because the question can easily because why do the Jewish holy texts not mention this figure? And my speculative answer is simply that the scope of Tanakh was, for some unknown reason, codified so that Alexander the Great seems outside of the scope. The histories we have and the prophetic texts which we have are largely dealing with pre-exilic realities and the final books concern the restoration of the people to the land and the rebuilding of the Temple. One could hypothesize that these were deliberate choices made by the priestly class, but we do not know if this is the case. One could assume there is a narrative unity that ultimately runs thought the Old Testament, but this would also be speculation. And would open the question as to why the canon was codified in such a way, why did their canon close when it did?

And part of this issue is simple: the process by which some texts are codified and others are not is not a clear process. Brennan W. Breed, in Nomadic Texts: A Theory of Biblical Reception History, discusses the fluidity of text in the Second Temple period: even if certain texts were agreed to be holy which version of that same text was considered authoritative was not agreed upon (in a modern analogy it'd be like if I decided to read from The Message in my church, where Scripture reading is explicitly done from either the New International Version or the New Revised Standard Version; The Message is not seen as an adequate representation of the word of God, but in other churches it might be). Yet Breed's argument makes this conversation even more difficult. Because he also is pretty firm on the idea that the idea of a canon is an anachronistic category to impose upon ancient Judaism (p. 48-9) and highlights the variety of textual traditions and differences in which "the earliest version [of a text] was both copied and altered by... successive communities, each with their own distinction theological perspective" (p. 21). Which only highlights: why do we not know of Judaic traditions who were engaging in this process with their religious texts to decry or praise Alexander the Great? Why is it not until after his death that Judaism seems to find him particularly noteworthy?

Which also highlights why this issue becomes even more bizarre: there is not a monolithic Judaism that we can look to the past and say "there, that's THE Judaism." We know there was a plurality of Judaisms with people that were writing. We find manuscripts or references to texts that we do not have, we have competing views of what counts as the Old Testament (is 1 Maccabees a holy text or not?), yet we do not find more references. Did Alexander the Great not strike the Jewish people as noteworthy? Was his reign simply in an era where the Jewish people were, by and large, not writing too many works? Were works referencing him largely lost? Are there perhaps coded references to him in texts (akin to how Rome might be referenced through allusions and metaphor in later apocalyptic texts)?

(Added: to that last question, some do believe that Daniel contains obscure references to Alexander the Great:

ALEXANDER THE GREAT -- the king of Macedonia, the great conqueror; probably represented in Daniel by the “belly of brass” (Dan. 2:32), and the leopard and the he-goat (7:6; 11:3)

from M. G. Easton, Easton’s Bible Dictionary (New York: Harper & Brothers, 1893); it's an assertion I've come across elsewhere).

This is all a long way to say that I'm simply not sure if there's an answer we can get to. I think any answer will raise more potential question. It's a difficult answer to give, especially when Alexander the Great seemed to have made an impact with their neighbours.

Alexander is not mentioned directly in the Bible. However, he is mentioned multiple times. u/Jordandeanbaker has enlightened us in the book of Ezekiel. A prophecy about Tyre being destroyed which was fulfilled by Alexander. However, this does not qualify as a "mention." Along these same lines, Zechariah ch. 9 tells of a prophecy involving Tyre, Sidon, and Damascus. Specifically to Tyre is Ze. 9:4 "Behold, the Lord will cast her out, and he will smite her power in the sea; and she shall be devoured with fire" (KJV). In fact, most of that chapter is a prophecy in which Alexander arguably fulfilled. Still, this does not qualify as a "mention."

In Daniel, we see Alexander through interpreting dreams. In fact, a great many powerful empires are described via strange animalesque creatures. Alexander is described a few times. Keep in mind, these are subjective to interpretation. In Daniel 2, Daniel interprets Nebuchadnezzar's dream. Daniel 2:31-35 describe the statue of gold, silver, iron, bronze, and clay.

" Thou, O king, sawest, and behold a great image. This great image, whose brightness was excellent, stood before thee; and the form thereof was terrible. This image's head was of fine gold, his breast and his arms of silver, his belly and his thighs of brass,His legs of iron, his feet part of iron and part of clay. Thou sawest till that a stone was cut out without hands, which smote the image upon his feet that were of iron and clay, and brake them to pieces.Then was the iron, the clay, the brass, the silver, and the gold, broken to pieces together, and became like the chaff of the summer threshing floors; and the wind carried them away, that no place was found for them: and the stone that smote the image became a great mountain, and filled the whole earth." (Dan. 2:31-35, KJV). "Broken to pieces" and "carried away," but the image "filled the whole earth." Alexander's empire filled the earth and was made of many parts, but eventually was broken to pieces and withered away.

Daniel chapter 7 reveals Alexander again, in the form of a leopard: " After this I beheld, and lo another, like a leopard, which had upon the back of it four wings of a fowl; the beast had also four heads; and dominion was given to it" (Dan. 7:6, KJV). In the beginning of this chapter, four beasts are mentioned which are, in fact, empires. We interpret this to be Alexander because of the order in which it is mentioned and the number four. As you will see, Daniel uses this number often when describing Alexander.

Next, in Daniel chapter 8, Daniel talks about the ram and the goat. Daniel 8:2-8 describes a conflict between a ram with 2 horns (one higher than the other) and "an he goat" with one "notable horn." "And as I was considering, behold, an he goat came from the west on the face of the whole earth, and touched not the ground: and the goat had a notable horn between his eyes."(Dan. 2:5, KJV). Alexander did come from the West and he did take the whole world. Daniel explains the creatures in 8:20-21: "The ram which thou sawest having two horns are the kings of Media and Persia.And the rough goat is the king of Grecia: and the great horn that is between his eyes is the first king." Thus, we are to interpret the he goat as Alexander. At the end of the dream description, or at least the part that involves Alexander, the goat's horn was broken into four pieces, Dan. 8:8 (AGAIN). Dan. 8:22 explains that those four horns are the four kingdoms that rose up from the king of Grecia's empire. One thing to note here, Daniel interprets the goat as the King of Greece (Alexander III) and the horn as "the first king" (Phillip II).

Finally, Daniel chapter 11 mentions Alexander once more. Dan. 11:2-4 talks about three kings in Perisa and one mighty king in Grecia. But, Daniel, as he has always done, concludes with the empire being broken into four kingdoms. " And when he shall stand up, his kingdom shall be broken, and shall be divided toward the four winds of heaven; and not to his posterity, nor according to his dominion which he ruled: for his kingdom shall be plucked up, even for others beside those. (Dan. 11:4, KJV).

I know this answer comes a bit late, but I wanted to add to the answers. Someone put up a great post about Maccabees, so I left that out. I hope this helps.