"Last time when they met in Buenos Aires, Trump told Erdogan that they have been working on that, but we need to see concrete steps because it's been already two years, almost three years," Mevlut Cavusoglu told CNBC's Hadley Gamble at the Doha Forum on Sunday.

Turkey's government has demanded Gulen's return since the failed Turkish coup of 2016, which it accuses the cleric of orchestrating.

Turkish cleric and opponent to the Erdogan regime, Fethullah Gulen, at his residence in Saylorsburg, Pennsylvania on July 18, 2016.

A former ally of President Recep Tayyip Erdogan, Gulen has lived in self-imposed exile in the U.S. for nearly 20 years. He denies any involvement in the coup attempt, which saw rogue Turkish military personnel commandeer helicopters, jets and tanks, attack parliament and seize television stations.

Political analysts suspected Trump might use Gulen as a bargaining chip in exchange for Turkish compliance in the scandal of Jamal Khashoggi. Turkish authorities accused Riyadh of complicity in the murder of the Saudi journalist in its Istanbul consulate on October 2. Trump has refused to blame the Saudi Crown Prince, whom he sees as a vital Middle East ally, which led some to believe that he would be more amenable to Turkish demands in exchange for Erdogan's easing off the case.

But Trump told press last month that he was not considering extraditing the preacher to meet those ends.

The case of Gulen is a primary sticking point between the NATO allies, Cavusoglu said, along with Washington's support of Kurdish paramilitary forces in Northern Syria, which Turkey associates with the PKK, Kurdish separatists who have carried out numerous terrorist attacks on Turkish soil.