The Blues are currently short on central striking options, with Fernando Torres facing a spell on the sidelines through injury.
The Spaniard’s absence will leave ‘The Special One’ with only summer arrival Samuel Eto’o and the out-of-favour Demba Ba as his orthodox options for the position.
As a result, Mourinho is keen to draft in a top class forward and has set his sights on the French international.
The pair worked together at the Bernabeu, and the now Stamford Bridge chief is still thought to be a fan of the ex-Lyon man’s abilities.
Benzema’s future at Real is far from clear, with new boss Carlo Ancelotti thought to be unconvinced by his contributions so far.
The La Liga side are also tracking Liverpool’s Luis Suarez and may need to sell in order to raise funds for the Uruguayan.
Although Benzema has failed to find the net is his last five top tier appearances for Real, he has an impressive goalscoring record of 47 in 97 outings in the white shirt.
Could Karim Benzema fire Chelsea to the title?
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