EXCLUSIVE | By Arsenal correspondent Tony Hughes

Arsenal face a battle to convince Karim Benzema to leave Real Madrid and make a sensational switch to Emirates Stadium, Football Insider sources understand.

The Gunners have made a lucrative contract offer to the Real Madrid star after holding discussions with Benzema’s entourage in a bid to entice him to Emirates Stadium.

Real are prepared to listen to offers of above £40million for the France international as long as they can secure a replacement.

But sources close to the situation have told Football Insider that the player is yet to be convinced that Arsenal would represent the right career move.

Benzema harbours doubts as to whether the Gunners can match his ambitions of competing for the major honours even though they have won consecutive FA Cups and are regarded as a team on the up.

The Frenchman has been used to competing for the Champions League and La Liga titles every season, and has expressed private concerns as to whether Arsenal can reach the same level.

The Premier Leeague club are still working on a deal to sign the striker, although there remains work to be done to persuade him to make what would be a shock move from Spain to north London.

Benzema, 27, is the first-choice centre-forward at the Bernabeu and will only be allowed to leave if a proven alternative is signed.

As revealed by Football Insider,  Arsenal have identified Benzema as the type of “exceptional player” that Arsenal Wenger has said he is looking for.

Benzema’s agent Karim Djaziri has publicly ruled out a move, as has new Real boss Rafael Benitez, but behind the scenes Arsenal have not given up hope of enticing him.

Any transfer would not take place until the latter stages of the window but Wenger is a big admirer of Benzema and would be interested in making a club-record bid if he learned that there would be a strong possibility of signing him. For now, Wenger is prepared to play a waiting game and see if the front man becomes available.

Wenger has made it clear that he wants to make a significant forward signing this summer only if it is a player he regards as world-class and who would immediately strengthen his first team.

There is a possibility that Olivier Giroud could leave Arsenal if the Londoners could pull off what would be one of the summer’s most sensational deals.

Benzema has scored 134 goals in 281 matches for Real since joining the club from Lyon in 2009. He has been a regular starter in the spearhead role since Gonzalo Higuain joined Napoli two years ago, forming a productive alliance in a front three with Cristiano Ronaldo and Gareth Bale.

He has attracted strong interest from Premier League clubs, with Manchester United manager Louis van Gaal among those who is also closely monitoring him.