There is a post on /r/todayilearned that claims Alexander was a monotheist as a result of Aristotle's teachings. The page the post links to doesn't seem to have any sources, it sounds kinda like bullshit to me.
Having read Arrian and Plutarch, I was under the impression that Alexander was conventionally pious. He certainly is said to have dedicated altars to the gods of the Olympian pantheon on many occasions, something that cost him time and money. He consulted famous oracles, not something that a newly converted monotheist would seem likely to do. He made no new religious foundations, as far as I know, nor am I aware of any record of his having said anything about there being only one god. This sounds like a bizarre thing to me.
I'm not well-versed on Alexander the Great, but I do know that Herodotus believed Alexander I (ancestor to The Great) to be descended from a line of Herakles (i.e. descended from Zeus), although the passage has been read as connecting Alexander to Helios instead of Zeus (Histories 8.137-9). Herodotus was considered unreliable even in antiquity though (see Lucian). (Edit: I might also add that Alexander the Great is occasionally represented as Helios.)
While you wait on a historian better-versed on Alexander the Great, this article discusses a supposed correspondence between Alexander and Aristotle (the document in question dates no earlier than 6th century AD). I don't have access to the article to read it though.
What I can tell you is that a lot of myths exist around Alexander the Great. He appears in Jewish legend as having gone to Jerusalem and offered a sacrifice to Yahweh. (You can read Josephus's account in translation here, and see some scholarship on that passage here and here.) He also appears in 1 Maccabees as a purely historical marker.
He shows up in the Quran as Zul-Qarnain (the Two-Horned one) in Surah 18:83–97. This was a common title for Alexander, but that doesn't mean everyone agrees Zul-Qarnain was Alexander. (See here and here.)
Edited for clarity. Thanks to /u/Watermelon-Sugar for reminding me not everyone is steeped in Ancient Greek genealogy.
There is kind of an interesting story which might answer your question (though it may just as well have been Alexander being a smart-ass). Before being tutored by Aristotle, he was taught by a man named Leonidas. When Alexander was a child he once used two fistfuls of incense on the altar-fire as sacrifice to the gods. This caused Leonidas to lecture Alexander on not being wasteful, and that only when he had conquered the spice-bearing regions he could throw in as much incense as he wanted.
Fast-forward a few years and Alexander ends up doing just that. Along with the usual gifts to his mother and sister he gifted 18 tons of frankincense and myrrh to his old teacher, along with the admonition that one should not to be 'parsimonious towards the gods.' While it is difficult to ascertain something like one's beliefs from one quote, it would seem that he might be attributing some of his military success with favor from the gods.