The Spaniard has long been chased by the Serie A giants, and his future remains uncertain at Stamford Bridge.
Fabregas initially struggled to make an impression on Antonio Conte, but has featured more during 2017.
However, according to the Mirror, the Italian boss is still expected to listen to offers for Fabregas, who turns 30 next month.
Cesc Fabregas is still hoping to have a future at Chelsea under Antonio Conte
The Chelsea star is determined to remain part of Conte’s plans
The creative playmaker will have two years remaining on his expensive £156,000-a-week contract by the summer.
And even though the Chelsea star is determined to remain part of Conte’s plans, the manager is open to selling ahead of a potential revamp in west London.
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Antonio Conte is planning for big changes in Chelsea's midfield this summer
The Blues boss is looking to make changes in midfield at the end of the season, despite title glory being on the horizon.
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Fabregas leaving for Milan could be part of those alterations.
Claims over the last week have suggested the San Siro outfit are in contact with Chelsea over a deal, and that a verbal agreement has already been reached with the player.