This article from the Met describes the relationship between Venice and the Ottomans. Here’s an excerpt:

The Ottomans sold wheat, spices, raw silk, cotton, and ash (for glass making) to the Venetians, while Venice provided the Ottomans with finished goods such as soap, paper, and textiles. The same ships that transported these everyday goods and raw materials also carried luxury objects such as carpets, inlaid metalwork, illustrated manuscripts, and glass. 

Another article from the Met discusses Ottoman textiles in particular like the one above.