In Anthony Doerr's Cloud Cuckoo Land (not really a major spoiler but it comes right at the end of the book), >!Omeir, a 66-year-old Ottoman who lives by himself nine miles from the nearest village in what is now Bulgaria, seems in 1505 dimly aware of the colonization of America: "He has heard [...] that the Christians have sailed ships to new lands at the farthest edge of the ocean where there are entire cities made of gold, but he has little use for such stories anymore."!< Is this realistic?
The Mediterranean world was a very well-connected one with much interaction - trade, diplomacy and, yes, war - between "the East" and "the West", so it's no surprise at all that the Ottoman world would be well aware of the first trans-Atlantic crossings by the early years of the 16th century.
You can see in one of my previous answers that the Ottomans were familiar enough with European cartographic works to produce their own maps of the Americas by 1513.
It does start to stretch credulity a bit to think that someone "nine miles from the nearest village" would know about these voyages, but it's certainly not out of the question. And it's worth mentioning that this region was a core part of the Ottoman Empire; the Ottoman capital was nearby at Edirne (Adrianople) just 50 years previous and was not far from the new seat of government in Istanbul. This was no backwater.
More can always be said (notably about the specific situation in rural Bulgaria), but u/PartyMoses and myself offer some answers to a similar question here. In a nutshell, it's plausible if that person had at least regular access to some information hub (family network, market place).