With the Blues missing out on Liverpool star Fernando Torres, Chelsea could be keen to improve their strike force, and Real are prepared to offer the France international and cash for Cole, according to the Daily Mail.
The England international is looking to reunite with former Blues boss Mourinho, and the Portuguese is desparate to strengthen the left-back position with one of the finest in the world.
But Mourinho may struggle to prise Cole from Stamford Bridge, with Ancelotti saying earlier this week that the 29-year-old would not be leaving under any circumstances.
Benzema move to Real from Lyon for £36 million last year, choosing to move to Spain instead of Manchester United, who were also interested in a move for the Frenchman.
Despite the big move to the La Liga giants, Benzema struggled in his first season with his new club, scoring only eight goals under former manager Manuel Pellegrini.
His poor season led to Raymond Domenech leaving him out of the France team that endured a disastrous World Cup campaign this summer, and the 22-year-old is keen to bounce back this season.
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