Not really, no. The Ottomans were more interested in expanding their influence in the Indian Ocean basin against the increasing Portuguese presence than they were in seeking out a role in the Americas—the potential of which was unknown at the time, and required them to sail through a strait (Gibraltar) controlled by their enemy, Spain.

The Ottomans were more interested in establishing trading partners than colonies. Local partners knew what they had, what was valuable, and didn’t require reinventing the wheel. I mean, it’s a hypothetical but if things had gone differently between Cortes and Moctezuma, or Pizarro and Ayahualpa, for example, it’s entirely possible that Ottoman trade envoys might eventually shown up looking to sign trade deals. But establishing remote settler colonies involved a lot of resources and it wasn’t really their thing.

Giancarlo Casale’s The Ottoman Age of Exploration is mostly about the battle for dominance over the Portuguese, but he does discuss the brief consideration (and dismissal) of seeing what the Americas might have to offer. Very readable book, I highly recommend it.