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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.