But according to Diario Gol, Real president Florentino Perez immediately rejected the bid, stating that it is way below his valuation of the player.
The 29-year-old has been in miserable form this season, scoring just four goals so far, with two of them coming in this week’s Champions League thrashing of Apoel Nicosia.
He’s been linked with a move to the Emirates for a number of seasons and despite his lack of goals, Perez still considers him one of the best strikers in the world.
Just one of his goals was scored in La Liga and there are rumours Real are set to undergo a complete makeover, with fellow attackers Cristiano Ronaldo and Gareth Bale also linked with exits.
Arsene Wenger is keen to bolster his attack, with contract rebels Sanchez and Mesut Ozil looking more and more likely to leave at the end of their current deals.
Benzema wouldn’t be a like for like replacement for Sanchez but he would provide Wenger with an enviable selection headache in attempting to fit him in the same team as compatriot Alexandre Lacazette.
Sanchez’ likely destination remains league leaders Manchester City, while Ozil is heavily linked with a return to Spain with Barcelona, although Jose Mourinho is keen for him to join his Manchester United project.
Following Saturday’s win over arch-rivals Tottenham, Arsenal are sixth in the Premier League.
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