Although he is contracted at the Bernabeu until 2019 and has netted 17 times this season, Madrid are claimed to be ready to listen to big-money offers for the Frenchman.
The reported reason for this is that Real Madrid are seriously considering a move to re-sign Alvaro Morata just a year after selling him to Juventus.
Juventus signed the Spanish striker last summer for €15.8 million but the deal supposedly included a buy-back option meaning they could re-sign Morata this summer for €22.2 million.
It has been claimed that the European champions have been closely monitoring 22-year-old Morata's progress, with the youngster having found the net on seven occasions.
Arsenal or Liverpool?
Benzema's future has been the subject of major speculation and both Arsenal and Liverpool have been linked with the France international for some time.
Liverpool are more in need of his goalscoring abilities given how poor Mario Balotelli has been in front of goal, with the Italian finally breaking his Premier League duck for the club this week.
Balotelli was a £16 million acquisition and would surely have to make way if Liverpool were indeed to pursue a move for Benzema.
Would Real Madrid really consider selling Karim Benzema? And, if so, will he end up at Liverpool or Arsenal?
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