The midfielder has fallen out of favour at Stamford Bridge since Antonio Conte came in and he is ready to move on.
Milan almost signed the Spaniard on loan during the summer transfer window, but negotiations broke down late on.
However, according to Calciomercato, Fabregas is closing in on a January move to the San Siro.
Milan have held preliminary talks with Chelsea and a loan fee of around £2.5m is currently on the table.
The Italian club are also willing to make Fabregas’ switch permanent next summer – if he plays a certain number of games for them.