Fabregas was strongly linked with a move away from Stamford Bridge during the January transfer window, but remained in west London and has since impressed for Antonio Conte.
In his 300th Premier League appearance against Swansea on Saturday, the Spaniard scored and provided an assist as Chelsea clinched a routine 3-1 victory.
Fabregas, 29, recently insisted he would remain at the Premier League leaders beyond the current campaign despite Conte’s tendency to start him on the bench.
But while the midfielder appears content with his role at Chelsea, Calciomercato say Serie A giants Milan hope to secure his services at the end of the season.
It is claimed the club believe Fabregas is the ideal man to build their side around and help Milan restore their image in Europe.
Ex-Arsenal man Fabregas has made 88 league appearances for Chelsea since signing from Barcelona in 2014.