The report claims the French international will be made available in January after the Spanish capital club have advised the striker's representative to find another club in the mid-season transfer window.
Madrid signed Benzema for £25m from Lyon and are looking for a fee of around £17m. The 25-year-old striker has been the target of criticism from supporters for recent poor performances.
Arsenal and Chelsea are both searching for a top-class striker, having missed out on several targets over the summer. The Gunners have Olivier Giroud leading the line, while the Europa League winners have Fernando Torres, Samuel Eto'o and Demba Ba as attacking options.
And Manchester United, too?
Meanwhile, Manchester United's Wayne Rooney, who has less than two years left on his contract, could emerge as a target for rival clubs, with United perhaps bidding to replace him with Benzema.
However, Arsenal and Chelsea remain the most likely destinations for Benzema, after United manager David Moyes confirmed his side will not invest heavily in January.
Madrid manager Carlo Ancelotti had earlier suggested that Alvaro Morata will be given a place in the starting lineup against Levante, forcing Benzema to the bench. However, the former AC Milan and PSG boss fielded the French striker during their 3-2 win over Levante.
Ancelotti revealed the youngster lacks experience but said that he has high expectations from the Spanish duo of Morata and Jese.
"Morata is good enough to start, obviously. He doesn't have the same amount of experience as Benzema, but he is young, very keen and has a lot of skill inside the area. Morata is very important for us, and he is doing very well." Ancelotti said.
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