The Daily Star reports that the Gunners are set to lodge an improved £50million bid for Benzema.
Benzema has been linked with a move to Arsenal all summer and has previously insisted that he planned to stay in Spain.
But the French striker is now ready to move to the Emirates Stadium.
“It’s up to Arsenal to fight for Karim with a big offer,” a Real Madrid insider told the Daily Star said.
“Then he could be their player in this window.”