Speaking in Luxembourg, Kerry said Washington had not yet received a formal extradition bid for the expatriate cleric, but added: "We fully anticipate that there will be questions raised about Mr Gulen."
Gulen, a reclusive Islamic preacher with a worldwide following who is regularly accused of a behind the scenes role in Turkish politics, lives in a tiny town in the Pocono Mountains of the US state of Pennsylvania.
Kerry who spoke late yesterday to his Turkish opposite number Mevlut Cavusoglu by telephone, said: "We haven't received any request with respect to Mr Gulen.
"And obviously we invited the government of Turkey as we always do to present us with any legitimate evidence that withstands scrutiny and the United States will accept that and look at it and make judgments about it appropriately."
And, standing alongside Luxembourg's Foreign Minister Jean Asselborn outside the country's foreign ministry, he added: "I'm confident that there will be some discussion about that.