The account you are thinking of comes from Strabo, a Greek geographer and historian of the first century BC. In his Geography he relates how the people of Antium (a city subject to Rome) had been engaging in piracy which Alexander supposedly heard about and sent a letter demanding that Rome put a stop to such practices. A Roman mission to Alexander at Babylon in 323 is mentioned by Arrian in his account of Alexander's campaigns but he casts doubt on it. He says the story comes from two previous histories of Alexander (both lost now) and is not mentioned in either of the contemporary accounts he was using as his main sources. He goes on to say that the story of the Roman embassy states that Alexander was fascinated by Rome and inquired extensively about their constitution while also predicting Rome's future glory. Arrian doubts that the Romans would send a mission to such a faraway place, especially one ruled by an eastern despot. If we believe Arrian, then both accounts have a strong tinge of later Roman self-aggrandizement being inserted into history rather than actual historical events.

However it is interesting to note that Arrian mentions other diplomatic missions received by Alexander in Babylon around the same time. He states that embassies came from the Bruttians, Lucanians, and Tyrrhenians to pay homage to Alexander. The last one is interesting as the Tyrrhenians are mentioned by Strabo as co-operating with Antium in the previously mentioned piracy. Although these people would have had to have come from just as faraway as the Romans Arrian does not spend any time doubting whether or not these missions really came to Babylon. However there is some indication that these people would have been aware of Alexander. Livy relates how Alexander's relative, Alexander I of Epirus, responded to a plea for aid from the Greek city of Tarentum against threats from the Lucanians and the Bruttians (this was about the same time the other Alexander was setting off for Asia). He is alleged to have made a treaty of friendship with Rome but died before it could do much good. In any case, his intervention may well have brought news of Alexander's Asian exploits and the tribes he fought against may have thought it good to try and get on good terms with the great conqueror. Even so, it's hard to envision some Italian tribesmen going all the way to Babylon for such purposes. As far as the Romans are concerned, Livy doubts that they had even heard of Alexander when he was alive.

Where does all this leave us?The historical evidence of Roman contact with Alexander is scarce, vague, and is undermined by the implausibility of what was then a regional Italian power sending diplomats to a foreign king half a world away. They may have heard about him second hand through the Italian tribes who had fought Alexander of Epirus but I can't see it going much further than that. For Alexander himself, outside of Strabo the only mention of Alexander's supposed knowledge of anything close to Italy is found in his so called "Last Plans", a ridiculously grandiose account of what his aims were at the time of his death.

Ultimately, it's unlikely that Alexander knew anything about Rome. The evidence that states otherwise is difficult to corroborate and hard to believe. It's possible that both sides had some vague indications of the other's existence but anything else strains the limits of credulity. Maybe Alexander had heard about his Epirote relative's exploits in Italy before he left and had thus become aware of Rome. But Strabo's passing mention of his alleged contact with Rome is not, at least in my view, sufficient to prove that Alexander knew about Rome either before or after his great Asian campaign.