They really were in the wrong place geographically to reach the Americas. The only way to reach the Atlantic was either via the Straits of Gibraltar or sail around Africa.

This is not to say that the Ottomans did not have a global strategy of sorts. The Ottomans in the 16th century tended to gravitate towards expanding their power in the Indian Ocean through trade and alliances. This is emblematic of a wider expanse of vision beyond the Mediterranean basin and the Levant, the traditional bases of Ottoman power. The Ottoman court showed a new interest in cartography and a desire to dominate the spice trade. This was comparable to the motivations that drove the Spanish and Portuguese during the opening phases of American colonization.

Source

Casale, Giancarlo. The Ottoman Age of Exploration. Oxford: Oxford University Press, 2010.

One other book, a novel, is worth mentioning on this topic. The book White Jacket was published by Herman Melville in 1850. It was the novel preceding his tome, Moby Dick. It is not your standard novel in the sense that plot takes a serious back seat to setting, use of world, political agenda, and historical accuracy. It basically retells the adventures that Melville had onboard an American Man-of-War during the 1840s and is done in such a way that every nuance of the experience from start to finish is noted in detail. For example, just some chapter headings include: Theatricals in a Man-of-War, A Peep Through a Port-Hole at the Subterranean Parts of a Man-of-War, The Chaplain and Chapel in a Man-of-War, Some of the Ceremonies in a Man-of-War Unnecessary and Injurious, A Man-of-War Library, Killing Time in a Man-of-War in Harbor, A Knave in Office in a Man-of-War, Publishing Poetry in a Man-of-War, An Auction in a Man-of-War - you get the idea.

This book is also somewhat credited with the abolishment of corporeal punishment on board U.S. Naval ships, which Melville criticizes (through his main character) as not only unnecessary but counterproductive.

It's not the most free-flowing of novels, nor is it a history book, but it's worth a read if you want details from an American Man-of-War from that era.