The New York Knicks center is accused of being a member of a terror organization.
"Sabah" - a daily pro-government Turkish newspaper - notes that Istanbul's chief prosecutor's office also prepared an extradition request for Kanter.
Sabah says prosecutors are seeking an Interpol "Red Notice" due to Kanter's alleged ties with Turkish cleric Fethullah Gulen, who was blamed by the Turkish government for masterminding a 2016 coup d'etat which failed to overthrow them, an accusation Gulen denies.
Kanter is accused of providing financial support to Gulen's group.
The eight-year veteran took to social media on Wednesday to refute the claims against him.
Earlier in January, the 26-year-old decided not to make the trip to London, England for the Knicks' game against the Washington Wizards due to concern about his safety.
Kanter has been outspoken about his opposition of Turkish president Recep Tayyip Erdogan and had his Turkish passport revoked in 2017 due to his alleged relationship with Gulen.