The US pastor, Andrew Brunson, has been held by Turkish authorities since October 2016 on charges of being a member of Gulen's group.
Ankara has repeatedly called for Gulen to be extradited to Turkey from the United States to face charges of ordering the failed coup bid.
Gulen, who has been living in self-imposed exile since 1999, strongly denies the accusations of involvement.
"They say 'give us the pastor'. You have a preacher (Gulen) there. Give him to us, and we will try (Brunson) and give him back," Erdogan said in a televised speech.
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Norine Brunson was freed shortly after her detention, but her husband was charged with being a member of the Gulen movement in December.
They ran a Christian church in the Aegean city of Izmir.
Erdogan hit back at criticism of the Turkish judicial system after some American officials urged Ankara not to mix the cases of Gulen and Brunson.
"What does that mean? That you have a judiciary, but we do not have a judiciary?" Erdogan asked with heavy irony.
"The person here (Brunson) is being tried. But the one over there with you (Gulen) is not being tried! He lives in a mansion in Pennsylvania!
A decree late August gave Erdogan the power to extradite foreigners in exchange for Turks under arrest or convicted abroad in "situations where it is necessary for national security or in the country's interests".
Norine, who has lived in Turkey for over 20 years with her husband, met with US Secretary of State Rex Tillerson during his visit to Ankara in March.
Last month, Tillerson said Brunson had been "wrongfully imprisoned" in Turkey.
Turkey had hoped for a resurgence in relations with its NATO ally when Donald Trump assumed the presidency.
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