That's according to the Daily Express, who report that Brendan Rodgers is willing to bide his time and move for the French international at the end of the season. Arsenal were linked with a £30m move for Benzema earlier this summer, but Liverpool are now the favourites.
Real Madrid extension
The French star only just extended his Real Madrid contract, which ties him to the Bernabeu until 2019. But if Carlo Ancelotti can snap up Radamel Falcao next summer at the conclusion of his Manchester United loan deal, the Italian may let Benzema leave.
The former-Lyon star endured a difficult goal drought towards the end of last season, which saw him linked with a summer departure. Arsene Wenger had Benzema on his transfer shortlist and watched him in action at the World Cup.
In the end, the Arsenal boss opted for Alexis Sanchez from Barcelona, and Wenger snapped up Danny Welbeck from Manchester United on deadline day.
Liverpool meanwhile raided AC Milan to sign Mario Balotelli as a replacement for the departed Luis Suarez. But with plenty of money still available, Rodgers may be tempted back into the market.
This January would be too early considering Benzema's new deal, and the Frenchman has started the season in positive fashion, scoring two goals so far.
Much will depend on what happens with Cristiano Ronaldo, as it's hard to imagine Real Madrid letting both Ronaldo and Benzema go in the same summer. Ronaldo has been tipped to return to the Premier League.
Liverpool take on West Ham at Upton Park on Saturday evening while Arsenal travel to Birmingham to face Aston Villa in this weekend's Premier League action.
Brendan Rodgers on Liverpool form