Arsenal boss Wenger: I tried to sign Beckham from Real Madrid
However Beckham opted to remain at the Bernabeu, a decision that was vindicated when he helped them win the title in the 2006/07 campaign - his final season with the club before linking up with LA Galaxy.
"David almost came to Arsenal a couple of years ago when things did not go too well during his first season with Real," Wenger told the Daily Express.
"I even met the people who took care of his career, but in the end, David decided to remain at Real."
Beckham is currently training with Arsenal in a bid to maintain his fitness ahead of England's upcoming friendly against Switzerland, although Wenger has already ruled out a loan switch.