Wenger, 65, is preparing for a 20th campaign in charge of the Gunners.
Having secured back-to-back FA Cup victories following a near decade without a trophy, Wenger now has the squad focused on a sustained challenge for the Barclays Premier League.
Gazidis believes Wenger, who last summer signed a new contract extension to the end of the 2017 season, remains the right man for the job as long as he feels able to do it.
"He's been incredibly important for us..
You never know, but he's in great health and he's doing incredibly well
He's full of energy and enthusiasm, his hunger is still there, and I'd never put an end-date on it," said Gazidis in an interview with the St raits Times
"He's also been a passionate supporter of the club, in a sense a fan of the club
He's put the club's progress and development above his own personal interest.
"We believe we have the right man in the club and we're very pleased that he's full of health and willing to carry us forward."
Arsenal have in recent seasons been able to land such marquee signings as Mesut Ozil and Alexis Sanchez, while earlier this summer they brought in veteran goalkeeper Petr Cech from Chelsea, who could play against Everton in the final of the Barclays Asia Trophy on Saturday.
Gazidis said the board shared Wenger's optimism about what the current group can achieve
He added: "We have got a growing sense of belief in our squad
We want to be more consistent going into next season
"We definitely have the quality in our squad to compete and win the league."
Source : PA