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The Real Madrid ace has been linked with a move away from the Bernabeu in recent months.
Real are keen to splash the cash after a hit-and-miss start to the season under Zinedine Zidane.
The Spanish giants are already five points behind Barcelona in the La Liga title race after just eight games.
And according to Spanish transfer outlet Don Balon, Real are ready for a shake up to bring in fresh faces.
They say the La Liga side could sell Benzema to Arsenal to make room for new signings.
Don Balon even say the Gunners have made an offer for the France striker, 29.
And Benzema is said to be keen to join Arsenal, with Real president Florentino Perez also backing the move.
Benzema has made just five appearances for Real in all competitions this time out, scoring one goal.
Former Barcelona striker Gary Lineker yesterday branded Benzema as overrated following Real’s 1-1 draw against Tottenham in the Champions League.
He tweeted: “Is it me or is Benzema a tad overrated?
“A goal every other game in a team as strong as Real Madrid is nada especial.
“Decent not great.”