The Reds have been linked with a move for the French World Cup star in recent weeks after losing Luis Suarez to Barcelona in a £75m deal.
Benzema has endured a difficult spell in Madrid, and was heavily criticised by sections of their supports for some shaky displays.
With Radamel Falcao a target for Los Blancos, he has been mooted as a player whom may be sold.
But even if Liverpool were to make serious inroads towards the forward, their efforts would be unsuccessful.
It is understood that the player’s representatives have let Liverpool know that Benzema would not consider Anfield as a destination, with the Merseysiders not in the elite band of teams he would like to play for.
Arsenal and Manchester United have also been linked with the £35m-rated 26-year-old, who is thought to be keen to stay at the Bernabeu.