Italian website Calciomercato is reporting that the Serie A giants are exploring the possibility of signing the 31-year-old midfielder, whose contract at Stamford Bridge is due to expire next summer.
Fabregas has found his playing time to be somewhat restricted this season under new Chelsea FC manager Maurizio Sarri.
The former Arsenal midfielder is yet to start a game in the Premier League and he has only made three appearances from the bench in the top flight so far.
According to the same story, an exit for Fabregas from Chelsea FC in January is looking possible as AC Milan begin to turn their attentions towards reinforcements.
Fabregas has scored one goal in a total of nine appearances for Chelsea FC in all competitions so far this season.
The former FC Barcelona midfielder will be keen to try and force his way into Sarri’s first team in the coming weeks as the hectic festive period in the Premier League looms large.
Fabregas will be hoping to be involved when Chelsea FC return to Premier League action on Saturday evening with a trip to Wembley to take on London rivals Tottenham Hotspur.
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