Halis Hanci, designated as Gulen's henchman, came to Turkey two days before the coup attempt, Xinhua reported.
He has distributed money to Gulen, who has been living in the US since 1999.
Turkish authorities earlier on Saturday detained Mohammet Sait Gulen, one of Gulen's nephews, NTV reported.
Turkish President Recep Tayyip Erdogan repeatedly demanded the extradition of the cleric and the government has filed an official request with the US for it.
The failed coup attempt, which began on July 15, was crushed the next day; at least 290 people, including more than 100 "coup plotters," were killed, authorities said.
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