The Spanish giants were heavily linked with a move for the controversial Uruguayan this summer, but failed to complete a deal.
Moves for Asier Illarramendi, Isco and Gareth Bale were prioritised, despite the 26-year-old having stated his desire to move to the Bernabeu.
Real are still thought to be keen on Suarez, but having spent close to £150m they are aware that they must raise funds before making a move.
As a result Benzema is likely to make way, with Carlo Ancelotti said to be unconvinced by the Frenchman.
Arsenal have long been linked with the ex-Lyon man, but Ligue 1 champions Paris Saint-Germain are likely to step in if there is a chance that he could leave the Spanish capital.
Liverpool have insisted that Suarez is not for sale, and are set to re-introduce him to their starting XI in two games’ time following his 10-match ban for biting Branislav Ivanovic – the latest in a long line of misdemeanours.
The versatile forward has apologised for his summer conduct, but is still said to be seeking a move away from Anfield in search of Champions League football.
Do Liverpool need Luis Suarez? Or should they cash in while his price is high?
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