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Rekik, 20, who joined City from Feyenoord on 2011, made just two appearances for City. He made his debut in September 2011 against Birmingham City in the Carling Cup before joining Portsmouth on loan in March 2012 for whom he made eight appearances.
He made his City Premier League debut in a 1-0 win over Reading in December 2012 before joining Blackburn Rovers on loan in February 2013, making a further five starts.
Rekik was loaned out to PSV Eindhoven for the 2013/14 campaign, earning his first senior Holland cap during a 2-0 win over France. He was also named in Holland's provisional 30-man World Cup squad by manager Louis van Gaal, though he didn't make the final group bound for Brazil.
Last season, despite being an unused sub in the FA Community Shield defeat to Arsenal, he was again loaned to PSV for the entire campaign he played 38 times as the Dutch side lifted the Eredivisie title.
Everybody at Manchester City wishes Karim the very best for the future.