The 25-year-old joined the Reds from Monaco before the season and has started four games in all competitions.
The report adds that Milan want to sign the Brazilian on loan, a similar deal to that of Chelsea star Tiemoue Bakayoko.
The Chelsea midfielder has struggled at the Serie A club and Milan are linked with moves for Eric Bailly and Gary Cahill from the Premier League too (h/t Calciomercato).
The Brazilian seemed a little slow in some of our earlier games but did a great job against Red Star Belgrade at Anfield.
Fabinho hasn’t been able to show his talent in the Premier League, however, it will be interesting to see how the Brazilian progresses in the coming weeks.
Liverpool have numerous fixtures coming up in the festive period, and the midfielder will get his chance to impress Jurgen Klopp prior to the winter break.
The Liverpool manager isn’t someone who cuts players after one transfer window and the Brazilian should have time to prove his ability to the Anfield faithful.
Trying to sell the 25-year-old after just one window would certainly lead to a loss for the Reds. Fabinho isn’t the only summer signing yet to star for Liverpool as Naby Keita spent almost the entirety of last month injured.