The 19-year-old, who joined the Blues in controversial circumstances three years ago, is out of contract at the end of the season.
There had been doubts about whether he would be offered a new deal as the west London club look to cut the wage bill, but French newspaper L'Equipe has revealed that a four-year contract is on the table.
Controversial capture: Kakuta (left) arrived at Chelsea from French club Lens
Kakuta was excused international duty last month to thrash out his future, though a move abroad could be even more tempting.
Bayern Munich have shown interest, but AC Milan have now emerged as a strong competitor.
Kakuta is concerned at his lack of first-team opportunities at Chelsea and would seek assurances from other suitors that he will get playing time.
His arrival at the Barclays Premier League club was contested by Lens in 2007. The 'tapping up' dispute led to Chelsea being banned from signing any new players until January 2011 when FIFA handed down their judgement in September 2009.
However, the Court of Arbitation for Sport overturned the decision in February and cleared Chelsea of wrongdoing.
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