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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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?