However he has not had the desired impact since his 2009 £35m move, and the Frenchman's physical and speedy style of play is arguably better suited to the Premier League.
Manchester United were so interested in signing Benzema when he was at Lyon Sir Alex Ferguson presented him with a club shirt after he scored against the Reds in the Champions League round-of-16.
Despite receiving £80m from Cristiano Ronaldo's world record transfer to Real in 2009, they decided against bidding for the Frenchman and instead settled for free transfer Michael Owen.
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Arsenal will play in the Champions League for a 14th season running
Arsène Wenger is under mounting pressure to reinforce an underwhelming squad at the risk of being usurped by north London rivals Tottenham this season.
Arsenal declined to sign Gonzalo Higuaín early in the summer as they focused on luring Suárez to the club.
They also contacted United about Wayne Rooney's availability, but the Suárez saga is now over, Wenger confirmed.
Arsène: From happy to unhappy
FBL-ENG-MAN CITY-ARSENAL(01 of10)
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Arsenal's Manager Arsene Wenger follows the pre-season match between Premier League giants Manchester City and Arsenal in Helsinki on August 10, 2013. AFP PHOTO / LEHTIKUVA / MIKKO STIG *** FINLAND OUT *** (Photo credit should read Roni Rekomaa/AFP/Getty Images) (credit:Getty Images)
Arsenal Training Session & Press Conference(02 of10)
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ST ALBANS, ENGLAND - AUGUST 20: Arsene Wenger, manager of Arsenal looks on during a training session ahead of their UEFA Champions League Play Off first leg match against Fenerbache at London Colney on August 20, 2013 in St Albans, England. (Photo by Matthew Lewis/Getty Images) (credit:Getty Images)
FBL-C1-EUR-FENERBAHCE-ARSENAL(03 of10)
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Arsenal's head coach Arsene Wenger looks on ahead of the UEFA Champions League Play Off first leg match between Fenerbahce and Arsenal at Sukru Saracoglu Stadium in Istanbul on August 21, 2013. AFP PHOTO/OZAN KOSE (Photo credit should read OZAN KOSE/AFP/Getty Images) (credit:Getty Images)
Arsenal v Aston Villa - Premier League(04 of10)
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LONDON, ENGLAND - AUGUST 17: Arsene Wenger of Arsenal looks on as a fan behind makes his feelings known during the Barclays Premier League match between Arsenal and Aston Villa at Emirates Stadium on August 17, 2013 in London, England. (Photo by Clive Mason/Getty Images) (credit:Getty Images)
FBL-ENG-PR-ARSENAL-ASTON VILLA(05 of10)
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Arsenal's French manager Arsene Wenger gestures during the English Premier League football match between Arsenal and Aston Villa at the Emirates stadium in North London on August 17, 2013. Aston Villa won 3-1. AFP PHOTO/GLYN KIRK == RESTRICTED TO EDITORIAL USE. NO USE WITH UNAUTHORIZED AUDIO, VIDEO, DATA, FIXTURE LISTS, CLUB/LEAGUE LOGOS OR LIVE SERVICES. ONLINE IN-MATCH USE LIMITED TO 45 IMAGES, NO VIDEO EMULATION. NO USE IN BETTING, GAMES OR SINGLE CLUB/LEAGUE/PLAYER PUBLICATIONS. (Photo credit should read GLYN KIRK/AFP/Getty Images) (credit:Getty Images)
Arsenal Training Session & Press Conference(06 of10)
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ST ALBANS, ENGLAND - AUGUST 20: Arsene Wenger, manager of Arsenal looks on during a training session ahead of their UEFA Champions League Play Off first leg match against Fenerbache at London Colney on August 20, 2013 in St Albans, England. (Photo by Matthew Lewis/Getty Images) (credit:Getty Images)
ISTANBUL, TURKEY - AUGUST 20(07 of10)
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Arsenal manager Arsene Wenger attends a Press Conference ahead of their UEFA Champions League Play Off match against Fenerbache at Sukru Saracoglu Stadium on August 20, 2013 in Istanbul, Turkey. (Photo by Stuart MacFarlane/Arsenal FC via Getty Images)
ISTANBUL, TURKEY - AUGUST 20(08 of10)
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Arsenal manager Arsene Wenger attends a Press Conference ahead of their UEFA Champions League Play Off match against Fenerbache at Sukru Saracoglu Stadium on August 20, 2013 in Istanbul, Turkey. (Photo by Stuart MacFarlane/Arsenal FC via Getty Images)
FBL-C1-EUR-FENERBAHCE-ARSENAL(09 of10)
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Arsenal's head coach Arsene Wenger looks on ahead of the UEFA Champions League Play Off first leg match between Fenerbahce and Arsenal at Sukru Saracoglu Stadium in Istanbul on August 21, 2013. AFP PHOTO/OZAN KOSE (Photo credit should read OZAN KOSE/AFP/Getty Images) (credit:Getty Images)
FBL-C1-EUR-FENERBAHCE-ARSENAL(10 of10)
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Arsenal's head coach Arsene Wenger (C) shakes hands with Fenerbahce's head coach Ersun Yanal during the UEFA Champions League Play Off first leg match between Fenerbahce and Arsenal at Sukru Saracoglu Stadium in Istanbul on August 21, 2013. AFP PHOTO/OZAN KOSE (Photo credit should read OZAN KOSE/AFP/Getty Images) (credit:Getty Images)
"Absolutely no chance of that," he said. "It is true that one bid for a striker did not work. That took a long time. We have to wake up from that now. I'm confident.
"The transfer market starts for me now and a lot of activity will happen between now and 2 September. It is like a poker game. People hold their cards as long as possible. In the end, they go for decisions."
A £10m offer for Yohan Cabaye was rebuffed by Newcastle United on Monday, but it is expected Arsenal will return with an improved bid.
Cabaye travelled to Manchester for Newcastle's opening game of the season at City on Monday, but was sent back to the north-east prior to kick-off after manager Alan Pardew admitted he had been unsettled by Arsenal's interest.
Arsenal have also been told they can "forget about" Juventus' Paul Pogba, who they enquired about.