Although the Ottomans were keenly aware of the new world from maps taken from Spanish traders as early as 1501 (and potentially earlier) there was neither the proximity nor the need for trade in the Americas. American goods flowed to Spain, Portugal, and France, and could then flow on to the Ottomans.

The Ottomans were much more focused at the time on subduing the Mamluks and bedouin tribes. These lucrative areas would provide invaluable trade in the control of critical areas of the Levant and Egypt (and later Mesopotamia and it's critical trade with India and the far east).

Realistically the Ottomans were far more focused on matters that were key to the empire, their own growth and colonies. Remember that the Russians and Ottomans both had colonies, as colonies are not just over seas territories but territories on your border that you are developing and integrating into the empire (siberia/north africa).

https://www.saudiaramcoworld.com/issue/199203/piri.reis.and.the.columbus.map.htm

Its not just a coincidence that the 5 major powers involved with the new world were Spain, Portugal, Holland, France and Britain, 5 countries with substantial Atlantic seaboards. Or that European powers with little easy access to the Atlantic never sought or were late to the party, Italy, Turkey, Austria/HRE, Russia, Sweden. Secondly the Ottomans mainly lived at one end of a large shallow sea. They never developed a significant deep water knowledge or interest. compared to the Atlantic countries. To get to the Atlantic meant a long voyage past a host of hostile entities (like the Venetians) before they then would have faced the Spanish and British around Gibraltar. Additionally, as the themanwhoknows... says, they had other occupations.