El Confidencial says it is Perez who is delaying talks over a new contract for the France striker, despite his impressive form last season.
Real board members also have their doubts over Benzema and have urged Perez to cash in, rather than hand the striker a new deal.
For the moment, the president is keeping his powder dry. Benzema was a personal gamble by Perez and continues to count on his full support.
But if Liverpool indicate a willingness to sell Suarez in the coming weeks, then the Frenchman is sure to be put up for sale.
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