Kanter is currently in the US, while his team prepares for a clash against the Washington Wizards at London's 02 Arena on Friday (NZ time). The 26-year-old didn’t travel over fears he could get assassinated for his opposition to the Turkish President Recep Tayyip Erdogan.
Turkish newspaper Daily Sabah reported that officials in Istanbul were seeking a 'red notice' through Interpol, asking the international police agency to detain Kanter and remand him to Turkish Authorities.
Kanter is accused of providing financial support to US-based Turkish cleric Fethullah Gulen, who is blamed for a failed coup in 2016. Since the coup attempt, some 77,000 people have been jailed pending trial and 150,000 state employees, including teachers, judges and soldiers, have been suspended or dismissed in a crackdown on alleged supporters of Gulen.
Prosecution officials could not be reached for comment, when contacted by the Associated Press.
Kanter responded to the reports on Twitter, claiming the Turkish government wouldn't find "a piece of evidence of my wrongdoing".
"I don’t even have a parking ticket in the US," he said. "I have always been a law-abiding resident."
Kanter followed up with a tweet saying: "The only thing I terrorise is the rim."
The Turkish native is a vocal critic of Erdogan and was detained in Romania in May 2017, after travelling there for charitable work. His Turkish passport has been revoked and Turkey issued an international warrant for his arrest.
Kanter has often called Erdogan "The Hitler of our century". On top of that, Kanter's father, Mehmet Kanter, was indicted last year and charged with "membership in a terror group".
Earlier this month, Kanter spoke out about his fears of travelling abroad, when he ruled himself out of contention for the match against the Wizards.
"Sadly, I'm not going, because of that freaking lunatic, the Turkish president," Kanter said. "It's pretty sad that all the stuff affects my career and basketball, because I want to be out there and help my team win.
"But just because of the one lunatic guy - one maniac, one dictator - I can't even go out there and do my job. It's pretty sad."
"They got a lot of spies there," Kanter said, when asked if he really believed he could die if he travelled to London.
"I can get killed pretty easy."
Kanter is good friends with Kiwi NBA star Steven Adams, as the pair played together at the Oklahoma City Thunder for two seasons.
The centre pairing became known as 'The Stache Brothers' for their trademark facial grooming.