Wenger, 62, has less than two years left in his contract and the club hierarchy are said to be mulling a contract extension in order to tie him down at the club.
The ex-Monaco coach has always had a healthy relationship with the club officials and is much-loved by the supporters even as he failed to win a trophy in the past seven years.
His attempts in recent times to bring silverware to the Emirates Stadium have been made difficult by the sale of key players such as Cesc Fabregas, Alex Song and Robin van Persie. Despite this, however, he has masterminded the club to an unbeaten start to the Premier League in the current season.
Gazidis stated that Wenger remains a crucial component of the club's long-term future and praised his value-driven approach to the transfer market and his puritan focus on attacking football. He stated his hope that Wenger could go on for a long time in charge of the north London club.
"It's not a sense of sentimentalism, not a reward for services, it's a belief that we have an incredible manager who loves this club and is the best man to lead us forward," Gazidis told the Telegraph.
"We're really confident about the direction that the club is heading. I feel he can keep going for a long time. He's in fantastic shape and he's as driven as he's ever been and excited as ever.
"It's fantastic to see his endless enthusiasm. I really have learnt from Arsene and the players learn from him as well.
"The values that Arsene has brought to the club together with the values that the club had before Arsene are what will inform us and give us the framework as to who might take over from him in the longer term. He is written into our DNA.
"As a club, we have to make sure that all of the things that Arsene has brought to the club are enshrined in our DNA to make sure that, when Arsene decides it's time, we are in a position to take his ideas and work forward.
"Arsene never succumbs. We're not dominated by fear.
"We try to do more than win, we try to win with style. I know we haven't won trophies in recent years. There's no one here that doesn't feel the pain of not being able to do that.
"We're very optimistic about this season. We're absolutely trying to win silverware and we're trying desperately hard to do it this year."
Gazidis also defended the club's decision to sell Song and Van Persie over the summer transfer window. He pointed out that Wenger's new signings can be trusted as the Frenchman has always brought value for money and has consistently delivered results towards the end of the season.
"We can get into extensive debate about individual decisions - and like all clubs we are not perfect - but the ultimate arbiter of whether you are spending your money efficiently is where did you finish in the Premier League versus your overall spending.
"When you look at what Arsene has done, within the overall constraints, he has outperformed our spending every single year he has been manager. It is extraordinary."
Gazidis also stated that the club are doing everything they can in order to boost their revenues and be part of the group of the top five richest clubs in the world in the near future.
"In terms of the financial impact, it [the new deals] will be as significant a step forward as the (Emirates) stadium was in 2005," Gazidis said.
"It does kick us into the top five clubs in the world with separation from the rest.
"The overall journey that the club embarked on was to make it one of the leading clubs in the world and to do it in a way that would be sustainable.
"We get accused of a lack of ambition or complacency because apparently the board are only interested in the top four. That is absolute rubbish.
"To me this is the most ambitious football club I know."
Arsenal next play Southampton on Saturday in the Premier League.