The sources noted that the U.S. Embassy had informed Turkish authorities about the matter.
The warships are currently anchored off the island of Crete, the most populous Greek island.
Turkish diplomatic sources on Friday shared that the United States had notified Turkey two weeks earlier that it planned to send two warships through the Turkish Straits toward the Black Sea in line with the Montreux Convention, adding that the vessels will remain in the Black Sea until May 4.
The move came as Russia bulked up its military presence on Ukraine's eastern border.
Russia annexed Crimea from Ukraine in 2014 and the two U.S. warships were due to arrive in the Black Sea this week amid an escalation in fighting in eastern Ukraine where government forces have battled Russian-backed troops in a conflict Kyiv says has killed 14,000 people.
The deployment came as the West sounded the alarm over what it says is a big and unexplained build-up of Russian forces close to Ukraine's eastern border and in Crimea. Russia has said it moves its forces around as it sees fit, including for defensive purposes.
The 1936 Montreux accord gives Turkey control over the Bosporus and Dardanelles straits. It also limits access to naval warships and governs foreign cargo ships.
