Well, the Greeks and Persians had a long history of conflict stemming back to before the battle of Marathon, when the Athenians mucked about with the Greek colonies (under Persian suzerainty) on the coast of Anatolia (Miletus etc), and through them burned the Persian district capital of Sardis. Then came the Greco-Persian wars, from Darius' invasion and the battle of Marathon to Xerxes' invasion and the battles from Thermopylae to Plataea. During the Peloponnesian Wars, the Persians mucked about with the Greeks, favoring first one side and then the other (primarily with financial support), before finally definitively funding the Spartan fleet and thereby allowing them to fight Athens at sea and finally win those wars. So there was a long history of conflict between the Greeks and the Persians which Alexander surely would have grown up learning about.

Moreover, his father Philip was building the Macedonian army into a very fine instrument for that very purpose of invading Persia. His father wanted to invade the Persian Empire himself, and indeed had attempted one invasion of Anatolia. His own ambitions were cut short by his assassination, but he would certainly have raised Alexander to hold similar ambitions.

A quick and dirty answer, I'm sure someone much more knowledgeable will be able to correct this rather general account and give you a proper answer in much more detail.