The Spaniard has struggled for game-time this season under new boss Antonio Conte and has inevitably been linked with a potential January exit.
Milan are currently in the midst of being taken over by their new Chinese investors and with the deal set to be completed by the middle of next month, they have already installed Marco Fassone as CEO and Massimiliano Mirabelli as their director of sport.
According to reports in Italy, both men were in the English capital on Saturday to discuss the possibility of a move for the World Cup winner.
The Rossoneri are without skipper Riccardo Montolivo for the next six months due to a torn anterior cruciate ligament and Fabregas could well slot into his role in midfield.
Chelsea may well be keen to sell the 29-year-old, with his form having diminished somewhat since helping the side win the Premier League title during the 2014-15 campaign.
Southampton have announced plans for a two-week tour of China as part of their pre-season preparations for the 2018-19 season.