Because essentially there's no reason for them to do so. Columbus himself set sail for the west not to discover a new continent (whose very existence he repeatedly tried to disprove) but in search of an alternate route to the Indies. In much the same way, the Portuguese explorers who discovered Brazil did so accidentally while on their way to India, since only by sailing far into the Atlantic could they find winds that would carry them past the southern tip of Africa. Even as late as the seventeenth century, numerous Dutch, English, and French expeditions to North America were similarly done in search of a Northwest Passage to the Orient. Hence from The Ottoman's perspective at that time was a logical reflection that unlike for Europeans, the New World for them was not on the way to India. As a result, once they had successfully conquered Egypt (a prize for which the Spanish and Portuguese would have gladly traded all their claims in the Americas), the Ottomans quite reasonably took advantage of the Red Sea and Persian Gulf to gain access to the treasures of the East, rather than vainly searching the Atlantic for a shorter route that simply did not exist. With the benefit of our hindsight we know how valuable the New World would be, but at the age of exploration it wasn't that obvious. Said reports of wealth in the New World had only come during the 17th century, and by that time, it was too late and difficult to establish colonies in the New World. That doesn't mean the Ottomans weren't engaging in "colonial" ventures though. The Ottoman Empire in exchange tried to expand their influence and control trade routes in the Indian Ocean, executing their prestige and title as Caliph to battle the Portuguese and Spanish. The Ottomans even had an informal colony of émigrés in Gujarat

You can read more about the Ottoman's attempt at dominating the Indian Ocean (and also the source for this) in The Ottoman Age of Exploration