The Chelsea midfielder has fallen down the pecking order at Stamford Bridge since the arrival of Maurizio Sarri last summer.
Fabregas, 31, has not started a Premier League game under Sarri and has been used in Europa League games to give Jorginho, N’Golo Kante and Mateo Kovacic a rest.
The Spaniard is a free agent next year and can sign a pre-contract with an overseas club next month.
Football Italia claims Milan have met with Fabregas’ agent to thrash out terms.
The Italian giants led by new chief executive Ivan Gazidis and director Paolo Maldini are keen to add to the squad next month, have tabled a two-and-a-half year deal to tempt the Spaniard to Serie A.
Milan will push Chelsea for a cut-price fee next month know they will get nothing for him next summer.
Maldini has hinted that Milan could bag Fabregas and Zlatan Ibrahimovic in January.
The LA Galaxy striker has been heavily linked with a return to the San Siro, six years after leaving for Paris Saint-Germain.
The MLS side failed to make the end of season play-offs despite the big Swede’s 22 goals since his arrival in March from Manchester United.
Maldini told Sky Italia: “Fabregas and Ibra? We have ideas…”
“We want to do everything so we can finish in the top four and we’ll try to make signings, but we’re happy with this team regardless.
“Even those whose contracts are expiring are showing great professionalism.”
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