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.
What is your opinion? Feel free to discuss the article under. You have to comment by using your Facebook profile. Be fair and have respect for other people and opinions!
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.