Arsenal have long been interested in Benzema, whose future at Real Madrid remains uncertain.
The France international has enjoyed a fine start to the season - shining against Barcelona in the recent Spanish Super Cup - but his inconsistent form last term suggests he faces a battle to prove his worth.
Alexis Sanchez, meanwhile, continues to be linked with a move to Manchester City.
Arsenal have repeatedly insisted the Chile international is not for sale but Pep Guardiola is likely to try and prise him away from the Emirates before next week’s transfer deadline.
Arsenal are ready to swoop for Real Madrid hitman Karim Benzema if Alexis Sanchez leaves
And Spanish outlet Diario Gol claim Benzema is likely to join Arsenal as Sanchez’s replacement.
Should the 28-year-old join City, then Arsene Wenger is ready to swoop for his compatriot and pair him up top alongside Alexandre Lacazette.
The Gunners’ 1-0 defeat to Stoke at the weekend highlighted their need for more firepower, with Danny Welbeck toiling and Olivier Giroud ineffective from the bench against Mark Hughes’ side.
And Benzema could fit the bill, with a new lease of life perhaps the ticket to reviving his faltering career.
However, any move is solely dependent on Sanchez and what he decides to do.
GETTY
Arsenal want Real Madrid forward Karim Benzema to replace Alexis Sanchez
GETTY
Arsenal star Alexis Sanchez holds the key to a Real Madrid transfer for Karim Benzema
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Should he stay for one more season then any potential transfer will be off the cards.
Diario Gol add that should Benzema join Arsenal, then Real will do everything in their power to sign Monaco prodigy Kylian Mbappe.
The 18-year-old was high on their list of targets earlier this summer before manager Zinedine Zidane opted to delay a bid.
But, despite Paris Saint-Germain appearing to be closing in on a deal for the teenager, Real still harbour hopes of bringing him to the Bernabeu.