The England defender's return from injury in January has coincided with the club's re-emergence as title challengers and their run to Sunday's FA Cup semi-final with Wolves.
And Wenger hinted that Adams may have a role to play off the pitch at Highbury as well when he eventually retires. The former Monaco manager realises the importance of such continuity, having relied heavily on the advice and knowledge of his coach, Pat Rice.
Wenger said: "Without Pat I would have made many mistakes. He knows the spirit of the club, so I would say it's important to have players like Tony at the club.
"One day it will be important for the club to keep one or two of these players in order to keep this kind of spirit. There's great spirit in the team and a togetherness and a feeling of achieving something together.
"People who've played together for 10 years have something special between them. When I arrived here, I quickly got the feeling that Arsenal has a special spirit and these experienced players are responsible for it."
Adams is equally complimentary about the Frenchman's influence and has the highest respect for the part Wenger has played in prolonging his career.
The 31-year-old said: "We're talking about my contract. These things will take care of themselves, but I'm happy just playing football for this club.
"Arsene Wenger is a very intelligent man. He sometimes may appear detached and aloof, but he is watching. Some people with fear and insecurity could take that the wrong way if they're not confident, but he's impressed me with his knowledge and his great insight into other people.
"He's pointed out a few things to help me with my self-awareness, which I've realised can help me. He's an honest man. I think between us we've extended my career. He's given me every chance to do so. The way I was going there was not going to be much life left in me."
The renewal of Adams' partnership with Martin Keown, Lee Dixon and Nigel Winterburn in the Arsenal defence has played a major role in the club's excellent recent form. However, they will have to do without Dixon on Sunday, as the right-back is ruled out by a hamstring injury.
Wenger has several other major injury problems and admitted it would need "a miracle" for his striker Ian Wright to make the starting line- up.
"I believe in miracles," the Arsenal boss quipped. "After all, Lourdes is in France! Maybe we have to go there before Sunday.
"If I had to make a choice today, I would say he won't play, but I can't say definitely no. He has such a big desire to play. He was very down to start with, but at the moment he's happy because he thinks he's not far away."
The Dutch winger Marc Overmars is rated highly doubtful after picking up an ankle injury in the 1-0 win at Bolton on Tuesday, but Gilles Grimandi, who also injured his ankle at the Reebok Stadium, should be fit.Reuse content