Given their closeness to Italy it seemed that there would be some interaction (especially with Venice since they traded).
Genitle Bellini was a Venetian artist who was apart of a delegation to the court of Mehmed II in 1479. There was a 2005-6 exhibition of his art at the Gardner Museum http://www.gardnermuseum.org/collection/exhibitions/past_exhibitions/gentile_bellini_and_the_east?filter=exhibitions:3318
Columbia's Academic Commons has a recent dissertation by Nassim Ellie Rossi about the evolution of Renaissance depictions of the Ottoman Sultan http://academiccommons.columbia.edu/catalog/ac%3A161108