A Bola reports that Chelsea boss Jose Mourinho is keen to bring the stirker to Stamford Bridge.
Mourinho and Benzema worked together at Real Madrid, before the Portuguese manager returned to Chelsea.
Benzema has failed to score in his last five La Liga fixtures for Real Madrid.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.