This is a pretty interesting topic. You might like this old question: Why did the Ottoman Empire not pursue colonies in the New World as other major European powers did? . /u/OldWorldGlory breaks it down into different aspects and links to previous answers.

Well, the geography would have been a problem right away. The OE was located in a very unfavourable position for colonizing the Americas. Much further than any Colonial power, and also they would have had to pass by Spain and Portugal, two powers who wouldn't have had much reason to let an Ottoman venture succeed. While there was Ottoman privateering and raiding around North America in the 17th century, it was based on small captured Islands around England, and therefore had a much smaller journey to the New World. It was also based on raiding, rather than starting and supplying a new area of the empire. I do know that the Ottomans had the Sultanate of Aceh swear allegiance in the 16th century, but that seems to have been dissolved with a rulers death. A flaired user should be able to give you more detail