Don Balon claim the Hammers offered £60m for the Frenchman, but he has rejected the move as he believes, understandably, that it would be a backwards step in his career.
Benzema has made 27 appearances in La Liga this year but scored just five goals. Barring a late goal rush, this will be his first single figure tally since his first season at the Bernabeu back in 2009/10.
A major squad overhaul is expected at Real Madrid this summer, with Robert Lewandowski and Harry Kane their main targets to fill the centre forward role and take some of the weight off Cristiano Ronaldo's shoulders.
The signing of either player would probably knock Benzema down the pecking order, but the 30-year-old would rather stay and fight for his place than link up with West Ham. The £60m bid does show that the Hammers are prepared to flex their financial muscle though.
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A move elsewhere may be on the cards. Arsenal have long been fans of Benzema, but with Arsene Wenger leaving the club this summer that move now appears uncertain.
Since joining Real from Lyon in 2009, Benzema has made 404 appearances for Los Blancos and scored 189 goals. However, he has never truly been a fans' favourite, having always played in Ronaldo's shadow.
If he leaves the Bernabeu this summer, he will depart as a two-time La Liga champion and a three-time Champions League winner.