This is one of those questions that will be all speculation. It is my personal, academic belief that the Mongols did not have knowledge of Alexander the Great. Now, the reason I believe that is the Mongols did not have any written language until 1204. One of the greatest legacies of Genghis Khan is the written form of Mongolian. This article from the University of California Irvine argues that the Silk Road was an important route for early trading, but not much communication actually happened before the unification of the Mongol Empire under Genghis Khan in 1206. Of course, I'm not asserting that zero communication happened between the Mongols and travelers from the west. I'm only arguing that people probably didn't talk about the Alexander the Great because their either didn't have the knowledge or it didn't pertain to their business.

I just cannot find any evidence that suggests that the Mongols had knowledge of great conquerors before the time of Genghis Khan. Honestly, the only way that we would know that the Mongols knew about great conquerors would be if they wrote it down or if we could find it in the historical record. I've not been able to locate anything that suggests that it did. I'm sure that someone with more knowledge than I can give you a better answer to this question.

Just a follow up to this question, in the Netflix show Marco Polo, Kublai Khan compares himself to Alexander by saying that he (Alexander) founded some 20+ cities, and that Kublai now holds all of them. Is this true?

As some people have pointed out already, this one is mostly going to be speculation, but I'd have to guess that some Mongols undoubtedly would have had at least some knowledge of Alexander the Great and earlier conquerors. Remember that by the late 13th century the Empire was split into four distinct khanates, and while knowledge of someone like Alexander the Great may not have spread throughout the empire/impacted Mongol actions, I'm pretty confident some branch of the empire would have been aware of his achievements. I'm basing this on a couple of factors, one being that the Mongols used local knowledge quite often in their attacks, often asserting their dominance over the power in a region to attempt to secure surrender from the cities/kingdoms they were currently attacking. In Juvayni's "History of the World Conqueror" the Mongol's have a pretty good knowledge of the history of Baghdad when they lay siege on the city. Commissioning Juvayni to write the History, as well as writing "The Secret History" shows the Mongols were at least somewhat interested in history and Kublai further proved this by his interest in learning about Chinese Dynastic traditions when establishing the Song Dynasty. Mongol's often employed valuable people they conquered, (artisans, intellectuals, engineers, military strategists, etc.) and gave them significant roles in the Empire. It is very likely that local Mongol leaders, at the very least, learned local history and traditions through these locals they worked with. Additionally, it is relatively well documented that the Mongols knew of Jesus and Christianity (see Carpini "The Mongols whom we call the Tartars" for proof of Latin influence reaching karakorum), and I'd have to imagine they at least took some interest in tales of other major conquerors.

There is also a connection with the word iskandar. It is the Turkish and Persian name for Alexander. Especially for Alexander the great . one of the Turkish/mongol leaders of Persia had this name.