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Chief prosecutors in Istanbul reportedly have prepared an extradition request for Kanter, who responded to the report immediately via Twitter.
"Turkish Government can NOT present any single piece of evidence of my wrongdoing," Kanter wrote. "I don't even have a parking ticket in the US (True). I have always been a law-abiding resident."
Kanter struck up a connection with Kiwi big man during his time at the Oklahoma City Thunder.
There the two became known as the 'stache brothers' in reference to their moustaches.
Kanter's Turkish passport was revoked in 2017 and he refused to travel to London with the Knicks this week, claiming spies or other Turkish operatives could assassinate him.
The newspaper said prosecutors are seeking an Interpol "Red Notice" over alleged ties to Fethullah Gulen, blamed for a failed coup in 2016, and accusations that Kanter provided financial support to that mission.
A Red Notice is a formal request to locate and arrest an individual facing extradition.
The United States would have to comply with the request and likely would do so only in the event there is compelling evidence Kanter committed a crime that could be prosecutable in the US.