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Milan acknowledged for the first time the bid on their official TV channel Mediaset, which claimed City had bid 150 million euros (197.5 million dollars) for the former World Player of the Year and offered him a salary of 15 million euros (19.8 million dollars) a season.
"This is a delicate moment. There is an offer from Manchester City for Kaka and Milan are considering it," said Milan TV presenter Mauro Suma.
The club's assistant manager Mark Bowen had told the BBC that a deal was "very close", but an Arabian business website insisted that talks had broken down.
Kaka himself was quoted as saying that he was happy to stay at AC Milan if the club did not want to sell him, but he has given every indication in the past that he would love to play in the English Premiership at some stage in his career.
He is already one of the best paid players in the world and his spokesman Diogo Kotscho said it would not be money that would prove decisive.