WASHINGTON, Oct 7 (Reuters) - Turkey has made a request to the U.S. to buy 40 Lockheed Martin-made F-16 fighter jets and nearly 80 modernization kits for its existing warplanes, as the NATO ally looks to modernize its Air Force after the purchase of F-35 jets fell through, sources familiar with the matter said. The deal, worth billions, is still working its way through the Foreign Military Sales process which is subject to approval by the U.S. State Department as well as the U.S. Congress which can block deals. The people spoke on condition of anonymity to discuss the deal. "As a matter of policy, the Department does not confirm or comment on proposed defense sales or transfers until they have been formally notified to Congress," a spokesperson for the State Department said. The Turkish Embassy in Washington declined to comment. Ankara had ordered more than 100 F-35 jets, also made by Lockheed Martin Corp (LMT.N), but was removed from the program in 2019 after it acquired Russian S-400 missile defense systems. The decades-old partnership between the NATO allies has gone through unprecedented tumult in the past five years over disagreements on Syria policy, Ankara’s closer ties with Moscow, its naval ambitions in the eastern Mediterranean, U.S. charges against a state-owned Turkish bank and erosion of rights and freedoms in Turkey. The request for the jets will likely have a difficult time getting approval from the U.S. Congress, where sentiment towards Turkey has soured deeply over recent years, primarily due to Ankara"s purchase of the S-400s and its problematic human rights track record. Ankara"s purchase of the S-400s has also triggered U.S. sanctions. In December 2020, Washington blacklisted Turkey"s Defense Industry Directorate, its chief, Ismail Demir, and three other employees. Since then the U.S. has repeatedly warned Turkey against buying further Russian weaponry. But last week, Turkish President Tayyip Erdogan indicated Ankara still intended to buy a second batch of S-400s from Russia, a move that could deepen a rift with Washington. There is bipartisan support in U.S. Congress to push the Biden administration to put further pressure on Ankara, primarily over its purchase of Russian weapons and its human rights track record. Ankara has said it hopes for better ties under U.S. President Joe Biden. Reports of the Turkish request were first reported by Greek defense outlet