Wenger has long been linked with Benzema, but the 28-year-old striker has always remained loyal to Real when talking about his future.
Merca Futbol says the Gunners manager is still keen on the France international - despite signing a striker in the summer.
A £40m bid could be on the cards.
Arsenal are unlikely to succeed in their pursuit after FIFA upheld Real's transfer embargo for the next two transfer windows.
Zinedine Zidane's side are banned from recruiting players in January and next summer so would be unable to sign a replacement if Benzema left for north London.