Wenger's current deal expires in 2014 and Gazidis maintains that the French coach, who took over in north London in 1996, is "written into [the club's] DNA".
The chief executive expressed his confidence in the direction of the club despite their current trophyless run and insisted that the values Wenger had instilled since taking over would continue to be their foundation.
"It's not a sense of sentimentalism, not a reward for our 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.
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"At the same time, 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 the day comes when Arsene decides it's time to hang up his boots - I don't know what the expression is as a manager - that we are in a position to take his ideas and work forward.
"The values that Arsene has brought to the club together that the values the club had before Arsene are what will inform us - and I don't want to give any indication that this is happening - and give us the framework as to who might take over from him in the longer term."
Gazidis went on to hit out at the suggestion that the Gunners had failed to show the ambition needed to claim their first silverware since they won the FA Cup in 2005.
"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," he claimed. "To me, this is the most ambitious football club I know.
"We're trying to win. In fact, we try to do more than that, we try to win with style - we have a certain way of playing football that we take pride in. So again, it's a high ambition.
"I know we haven't achieved that in recent years. There's no-one at this football club that doesn't feel the pain of not being able to do that in recent years but absolutely that's what we're trying to do and we want to do it on a sustainable basis going forward.
"We're very optimistic about this season, even through the loss of a player as important as Robin van Persie.
"We went through some major challenges last season and yet still came near the top of the game. But it's not what we're aiming to do. We're absolutely trying to win silverware and we're trying desperately hard to do it this year."