The France international has been stuck in a goal drought for his country, while he's only managed two in seven league appearances for the Bernabeu giants so far this term.
And Mourinho is reportedly ready to offer him an escape route to Stamford Bridge in the winter window.
The Chelsea target largely shared first-team duties with Gonzalo Higuain last term under Mourinho in Spain, but still managed 11 goals and 11 assists from 19 starts.
Mourinho tried and failed to sign Wayne Rooney from Manchester United over the summer, and the report claims he's still seeking a big-name recruit for the January transfer window.
Despite the addition of Samuel Eto'o, the Chelsea boss does not feel comfortable mounting a title challenge with the crop of forwards currently at his disposal. Fernando Torres picked up an injury in the week - and has not exactly been lethal in front of goal - while Demba Ba has barely featured.
And the arrival of Gareth Bale to Real Madrid could spell trouble for Benzema long-term, with Cristiano Ronaldo likely to play through the middle and the Welshman in his current position out on the flank.
Over the summer, reports claimed Benzema could be available for a fee around the £40m mark.
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