James Jeffrey, who was also a former deputy national security advisor under the George W. Bush administration, was speaking at a conference hosted by the SETA think tank in Washington D.C. on Monday.
The senior diplomat also described as “embarrassing” the continued presence of Gulen on U.S. soil.
Gulen is wanted by the Turkish authorities on a range of charges stemming from the July coup attempt last year which cost 250 lives.
The Turkish government said the coup plot was carried out by the Fetullah Terrorist Organization (FETO) led by U.S.-based Gulen.
Turkish officials accused the Gulen network of plotting to overthrow the government as the culmination of a long-running campaign to infiltrate the country’s institutions including the military, the police and the judiciary.
In a response to a question about whether Gulen will be extradited, Jeffrey told the audience Ankara had asked for Gulen’s extradition but the U.S. administration had yet to give a response that Turkey would find acceptable.
“It is embarrassing the fact that Fetullah Gulen is sitting here in the United States,” Jeffrey added.
He predicted the legal process surrounding Gulen's extradition would continue for some time because of the nature of the U.S. court system.
Jeffrey claimed former President Barack Obama in general did not make decisions quickly and waited to have all the facts before taking action; this led to a delay from the U.S. in condemning the Turkish coup attempt at the outset.
"That was very unfortunate, because in circumstances like that, you have to act immediately and we did not,” Jeffrey added.