The trio allegedly planned to kill Bartholomew on May 29, the 560th anniversary of the conquest of Istanbul by the Ottomans, Today's Zaman reported.
Authorities started to investigate after an anonymous letter was sent to the Kayseri chief public prosecutor's office alerting officials to an assassination plot.
The suspect in custody was identified as Serdar A. The other two hadn't been named, the newspaper said.
The suspect in custody denied the accusations, saying he had traveled to Istanbul, where Bartholomew is based, to look for a job, not as part of any plot to kill the church leader.
"I do not know even where Bartholomew is living," Today's Zaman quoted him as telling police investigators. "I do not know what his title or job is. I just saw him in the media. I have no plans or intentions to kill him."
The newspaper said the suspect has a history of arrests that include threatening and racketeering. It also noted it is the second assassination plot against Bartholomew uncovered by Turkish authorities.