The 19-year-old, who joined the Blues in controversial circumstances three years ago, is out of contract at the end of the season.
AC Milan had hoped to convince the France Under 21 midfielder to turn his back on Chelsea.
Controversial capture: Kakuta (left) arrived at Chelsea from French club Lens
There had been doubts about whether he would be offered a new dealas the west London club look to cut the wage bill, but French newspaperL'Equipe revealed earlier this month that a four-year contract is onthe table.
Kakuta's arrival at Chelsea was contested by Lens in 2007. The'tapping up' dispute led to Chelsea being banned from signing any newplayers until January 2011 when FIFA handed down their judgement inSeptember 2009.
However, the Court of Arbitation for Sport overturned the decision in February and cleared Chelsea of wrongdoing.
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