Catkic was taken into police custody as part of the investigation into the group led by the US-based Islamic preacher Fethullah Gulen, it said.
He is accused of downloading and sending messages through the Bylock messaging app which authorities suspect was used by Gulen's supporters to coordinate the July 15, 2016, coup, Dogan said. Gulen denies involvement in the plot.
Catkic was taken to Istanbul police headquarters for questioning. According to the Sabah newspaper, his home was also searched.
Over 50,000 people are being held under arrest in the wake of the coup, a crackdown that has caused international controversy.
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The crackdown has also touched football, with the authorities issuing an arrest warrant for former star Hakan Sukur, who played a key role in Turkey's glorious run to third place in the 2002 World Cup. Catkic was also in that squad.
Sukur, also a former stalwart for Galatasaray, is now based in the United States.
Former international footballer Bekir Irtegun, who played 10 times for Turkey, was detained last month on similar charges but then freed, though he remains barred from leaving the country.
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