The Turkish justice ministry has demanded that US authorities arrest the preacher on charges of ordering and commanding the attempted coup.
It was the first time Turkey had formally asked Washington to arrest Gulen, who currently lives in self-imposed exile in Pennsylvania, Middle East Eye reported.
Ankara has on several occasions asked the US authorities to extradite Gulen, sending them documents which allegedly show evidence of his involvement in the putsch.
Early last month, an Istanbul court issued a formal arrest warrant for Gulen, who has denied any involvement in the botched coup.
When US Vice President Joe Biden visited Ankara several weeks later, he said he understood the "intense feeling" in Turkey over Gulen.
The US has "no, no, no, no interest whatsoever in protecting anyone who has done harm to an ally. None," he said.
"But we need to meet the legal standard requirement under our law," he added.