That’s according to Spanish outlet, Don Balon who claim the La Liga giants would consider a bid of £44m, with the Gunners desperate to find a replacement for the exit-bound Alexis Sanchez.
Sanchez is closing in on the end of his current deal with Arsenal and will be free to talk to other clubs in the New Year.
As for Benzema, the 29 year-old has been perennially linked with a move to The Emirates and could finally be snapped up by his longtime admirer, Arsene Wenger.
The Frenchman who has the best part of two years to run on his current deal has fallen out of favour at Los Blancos.
Benzema only made 23 La Liga starts last term and 29 appearances in total. He scored 19 goals over all competitions.
Gooners, would you take Benzema? Let us know in the comments…