According to a number of websites, Wenger contacted the 23 year old about a possible loan spell with the Gunners in a bid to revitalize his lack of form.
Benzema is regarded as one of the best young attackers in world football, but since moving to Madrid in 2009, the French international has not been as clinical as one would imagine.
However, Wenger has been a fan of the former Lyon star for a number of seasons now and attempted to sign Benzema two seasons ago, but a deal failed to materialize.
However, the Arsenal tactician is keen to acquire Benzema on loan for the remainder of the season or the first half of 2011/2012. The 23 year old has fallen out of favour with Real Madrid manager Jose Mourihno and a number of big name clubs such as AC Milan, Liverpool and Manchester United are interested in signing Benzema, with Liverpool and the Gunners rumoured to be the favourites.
The French forward is blessed with devastating pace and balance alongside a ferocious shot. Capable of playing as a striker, winger and a second striker, Benzema would fit the quick, slick style of play the North London giants boast.
Furthermore, Benzema shares a strong relationship with a number of the French Arsenal players such as Bacary Sagna, Samir Nasri and Abou Diaby.
With Russian dynamo Andrei Arshavin losing form rapidly, rumours that he could depart the Emirates for Juventus could see Benzema move.