The French international has been a transfer target of Arsene Wenger for some time now as he looks to bolster his attcking options.
Real Madrid are keen not to lose their star striker, especially after having some promising World Cup performances, so they are planning to extend his current contract.
In just two games for France in the World Cup, Benzema has scored three goals and has claimed two man-of-the-match awards and with just 12 months left on his current contract, the new European Champions will be keen not to lose the striker.
According to Spanish newspaper Marca, Real coach Carlo Ancelotti has made his intentions to keep the 26 year-old very clear and the Frenchamn will be part of his plans in the future.
With this in mind, Los Blancos are willing to offer Benzema a lucrative new deal to keep his temptations from joining other top clubs at bay.
If the Gunners cannot secure the Benzema deal, then their attention will turn to AC Milan frontman Mario Balotelli.
By Phil Wellbrook