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The 28-year-old was said to be close to a move to Maine Road two weeks ago, but the two clubs reportedly could not agree on the transfer fee.
However, City and Bordeaux revived talks earlier this week, and the Frenchman flew to England on Tuesday to discuss teams again.
"On Sunday night my agent Pape Diouf left me a message to tell me that I was on the verge of joining Manchester City.
"I took the plane to pass a medical on Tuesday morning, we sorted out the details and I went back to Bordeaux yesterday to cancel my contract with the club," he added.
"I went to say goodbye to my team-mates, Elie (Bordeaux coach Elie Baup) and to the president (Jean-Louis Campora)."