The Anfield club have been highly active in the transfer market so far this summer, and reports suggest they are not finished yet.
The Merseyside club are said to be aware of the reports over the weekend that Benzema may sign a new deal at the Bernabéu, but are still thought to be intrigued by the possibility of bringing the Frenchman to Anfield.
Liverpool have already signed attacking options Ricky Lambert and Adam Lallana this summer, and are on the verge of completing a deal for Loic Remy, after an £8million fee was reportedly agreed with Queen’s Park Rangers.
The Benzema link comes following the sale of Luis Suarez to Barcelona, with Brendan Rodgers supposedly wanting an A-list replacement for the Uruguayan.
But the report also suggests that Benzema will cost Liverpool big, with an estimated £40million price-tag for the former Lyon man, and a possible £200,000-a-week in wages.
Real Madrid are also unlikely to sell Benzema as they are now short in the out-and-out striker department following the sale of Alvaro Morata to Italian side Juventus. Benzema’s position will not be affected by the arrival of Toni Kroos and James Rodriguez, and is likely to stay in the Spanish capital.
The only potential deal on Madrid’s end that could see Benzema keen to switch to Anfield would be the arrival of Monaco striker Radamel Falcao at the European Champions. Falcao has been linked with a move to Real, and would all of a sudden jeopardise the future of Benzema were he to join Carlo Ancelotti’s men.
Liverpool could be in need of increased firepower for the coming season to replace Suarez’s contribution, but a deal for Benzema would depend on many different factors, not just the Reds' desire to land the Frenchman.