The Gunners are known to be on the lookout for a top-class goal-getter in the coming months after a botched move for Liverpool’s Luis Suarez saw them left with only Olivier Giroud as an orthodox and experienced option in the role last term.
Benzema has been a rumoured target for Arsene Wenger for some time, and his hopes of snapping up the Frenchman have been boosted in recent weeks amid talk that he is no longer needed at the Bernabeu.
The ex-Lyon star has just 12 months to run on his contract, which has led to talk that he could well be sold for a reasonable price.
Arsenal are understood to be ready to offer £25m when they sit down with Real officials, and are hopeful that their own desire to snap up a new striker may see them accept.
Suarez is seen as a top target for the Spaniards, while some rumours have linked them with Manchester City’s Sergio Aguero.