The Gunners boss, speaking at a press conference before the Newcastle game, paid tribute to the former-England captain following his retirement announcement.
And Wenger admitted he tried to sign Beckham before he agreed to join Paris St Germain.
"I was interested in signing Becks, it was always a pleasure to have him here," Wenger said.
"He gained everyone's respect. He had a natural humility."
Beckham trained with Arsenal twice during the MLS off-season when he was still on the books at LA Galaxy, and was linked with a short-term move to the Emirates Stadium.
The former-Manchester United star announced his decision to retire on Thursday afternoon, ending a 20-year playing career at the highest level.
As well as United and Real Madrid, Beckham also played for AC Milan, LA Galaxy and latterly Paris St Germain. He also retires as England's most capped outfield player with 115 appearances.
Wenger also confirmed during his press conference that he's in 'advanced' talks to sign Auxerre striker Yaya Sanogo. The France under-21 striker is one of the most highly-rated young players in the country.