The Sweden international and his agent Mino Raiola met with Galliani after the end of the 2011-12 campaign to discuss the 30-year-old's future at the club, and they told the Milan director that he wanted to stay put.
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Even though Galliani made the promise that Ibrahimovic would not be sold, the San Siro outfit opted to cash in on Ibrahimovic after all when PSG made them an offer, and the powerful attacker has since cut his ties with the official.
"Ibrahimovic really wanted to stay at Milan," Galliani was quoted as saying by France Football.
"I promised him that he would not be sold when he came to meet me accompanied by Mino Raiola at the end of last season. However, the board then had a number of meetings and we opted to sell him after all.
"He doesn't speak to me anymore since he has left Milan for Paris. I can't blame him, though, as I broke my promise."
Ibrahimovic has scored five goals in four Ligue 1 games since his move to the Parc des Princes.