Beckham, 38, who announced his retirement on Thursday, has had spells training with Arsenal but never played for the Gunners, and Wenger said: "I have a huge respect for his passion for the game, his huge commitment, his mental strengths because he was under a lot of pressure throughout his career, and his dedication. I think that is where he is an example."
Asked if he had ever been interested in signing him, Wenger added: "Yes I was, but it was at the period where we could not afford to pay him."
He added: "After that it was a question mark as well before he went to (AC) Milan, but he was in a position where we did not really need (players). It was always a pleasure to have him here for his attitude and behaviour, he gained respect from everybody through his dedication and commitment.
"What remains in your memory is his genuine commitment and dedication, his natural humility which he always had, that will stay forever. You forget sometimes if he has won this championship or that championship, but you never forget how he behaved, and that is a credit to him."
Tottenham manager Andre Villas-Boas described Beckham's standing in the game as "immaculate", and he said: "(He is) a sporting legend, a great, great career. For somebody who has such a high profile he has been immaculate as a sportsman and as a person.
"(He is) a great, great example. He has gone through the world's best clubs and achieved many titles. He is one of the great examples of good sportsmen in the world."
Wigan boss Roberto Martinez singled out Beckham's impact on Real Madrid's team of 'galacticos', and said: "He's been a football icon. I think he's had an incredible contribution wherever he's been.
"Probably the most significant one was the move he had at Real Madrid. At the time of the galacticos there couldn't be a harder moment to arrive and I thought he was an incredible ambassador for English football.
"For someone to be as adaptable as he's been and playing in different leagues like he's done is quite remarkable and I don't think you'll see many examples like that."
- Sports & Recreation