The Reds carried out an overhaul of their midfield and signed four midfielders in Dominik Szoboszlai, Alexis Mac Allister, Ryan Gravenberch and Wataru Endo last summer.
Endo has taken time to settle since joining Liverpool and has conceded that the intensity of the Premier League has shocked him.
Jurgen Klopp is looking to add more meat to his midfield in January and Liverpool have been tracking Frendrup over the last few months.
And it has been claimed that the Reds are prepared to go in with an opening bid to sign the midfielder in the winter window.
Liverpool are said to be ready to offer a deal worth £10m to Genoa for the 22-year-old midfielder.
He has been closely tracked by the Liverpool recruitment team and the club are now prepared to act in January.
Genoa signed the Dane from Brondby in January last year and he has featured 66 times for the club.
Frendrup has a contract until 2026 with Genoa and it remains to be seen whether they are prepared to lose him in the middle of the season.
