Cavusoglu made the comments in an interview with private broadcaster Haberturk TV.
Turkey says Fethullah Gulen, who has lived in self-imposed exile in the United States since 1999, was responsible for the July 15 coup attempt that aimed to overthrow the government.
Gulen denies the charge. Washington has said Ankara must first provide clear evidence of Gulen's involvement in the attempted coup and lawyers have said any extradition process could take years, Reuters News Agency reported on Monday.