Il Corriere dello Sport says the Reds have been linked previously with the Algeria international, who is thought to be involved in contract talks with the Serie A giants.
Liverpool may have made an offer to sign Bennacer, but it does not specify whether this is for January or in the summer.
The 25-year-old's contract runs out in 2024, with him set to enter the final 12 months of his deal at the end of the season.
It has also been reported that Bennacer is expected to enter fresh contract talks with Milan in the next few days. And despite apparently changing his representatives in recent weeks, he is still thought to “have the last word" on a new contract.