The Ottoman Empire knew about the New World by 1513.
The "Piri Reis Map", from that date, which was re-discovered in the Topkapi Palace in 1929, shows it. Piri Reis was a captain (later an Admiral) in the Ottoman Navy when he drew the map.
Conveniently, he gives an account of how he made the map on the map, so we know that as well as various Eastern sources, he had 4 Portuguese Maps and one map by Columbus, which he used as sources. The Ottoman naval intelligence was obviously on the job in the early 1500s.