By Arsenal correspondent Tony Hughes

Arsenal have not given up hope of signing Karim Benzema from Real Madrid before the transfer window closes, Football Insider sources understand.

The Gunners will hold fresh talks with Benzema’s camp this week in an attempt to agree a £40million-plus deal.

Benzema’s agent has claimed that the France international wants to stay at the Bernabeu and will not be leaving the club ahead of next Tuesday’s deadline.

Real manager Rafael Benitez also insists that the striker  is a key figure in his plans and he has no intention of allowing him to leave.

But the player’s future was given a fresh twist when he missed Real’s goal-less draw at Sporting Gijon on Sunday night with what the Spanish club claimed was an injury.

Benzema was subsequently pictured taking part in training with Real on Monday morning to give further ammunition to those who have claimed his future is in doubt.

Arsenal are running out of time to make what would be one of the headline Premier League deals of the summer but there remains hope from inside the club that it can still happen.

Arsene Wenger has been given the green light by the Gunners’ board to make a club-record £45million offer for the Real Madrid star if they can convince him to make a sensational switch to Emirates Stadium.

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

Privately, 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 concerns to friends as to whether Arsenal can reach the same level.

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 Wenger has said he is looking for. Speaking last Friday, the manager admitted he is still in the market but claimed it is difficult to buy leading players at this stage of the window.

With Danny Welbeck out injured with a knee problem that has proved more serious than originally anticipated, a Benzema transfer is unlikely to mean Olivier Giroud now leaving Emirates Stadium.

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.