The Gunners have been linked with a move for the forward but it will be a costly one to engineer.
Arsene Wenger is reportedly keen to add a top class centre forward to his squad for next season, as he eyes a potential Premier League title challenge.
Benzema is top of the list, with the club having looked through a number of other targets and decided that the Frenchman is his number one priority, although he is aware it will be a difficult task to convince Madrid to sell and Benzema to agree to a move to the Emirates.
And according to AS, Wenger has deliberately played down any links of a move for the striker as part of his transfer strategy, with him keen to divert attention and potential rivals for his signature.
Benzema may fancy a move to the Emirates
Benzema himself may also fancy a move to England, with his future at the Bernabeu somewhat unknown under new boss Rafa Benitez.
It has been suggested the Spaniard will look to shake things up at the club next season by converting Cristiano Ronaldo into a true number nine, so as to accommodate him, Bale and James Rodriguez all in the same side.
A move to Arsenal would also be favourable as there are currently since Frenchman currently on the books, while it would also mean a reunion with Mesut Ozil.
He would also be guaranteed first team football with the Gunners, with Olivier Giroud unlikely to be chosen ahead of him. If Arsenal were to manage to strike a deal, it would certainly be a major coup and a big step towards the title, although a potential move is far from being completed at this stage.