Fabinho only left Monaco to move to Liverpool during the summer, and the Brazilian has slowly established himself in the team with five starts and three substitute appearances coming in all competitions.
However, speculation persists over the 25-year-old's future, and according to Corriere dello Sport, Milan are interested in securing a deal in the January window.
The Italian giants are likely to be in the market for a new central midfielder at the midway point of the campaign, and it appears that Fabinho has been identified as a possible signing.
The versatile South American still has over four-and-a-half years on his contract, leaving Milan in a position where they are only likely to be able to sign Fabinho on a temporary basis.
However, Liverpool boss Jurgen Klopp is unlikely to give the green light to Fabinho's exit while the club are competing on both the domestic and European front.