Wenger this month celebrated 18 years as manager at Arsenal, who need look no further than Manchester United and life after Sir Alex Ferguson to see how difficult it is to replace such a pivotal figure at a football club.
The Frenchman, who is 65 next week, signed a three-year contract extension in May after ending a nine-year trophy drought by winning the FA Cup.
Gazidis told Arsenal Media: "So much of the attention on a football club is around an individual and that's very understandable at Arsenal because we have a giant who's managing us.
"Arsene has been a fantastic driver and has put the club in a great, great position
The biggest challenge we're going to face as a club is that, when that transition from Arsene to the next manager of our football club happens - and I don't know when that's going to be - that we come through that strongly."
Gazidis, who has been in the post for six years, is optimistic for the future and wants Arsenal to join the world's elite.
"I wouldn't be doing this job if I didn't believe we could compete at the very top level," he added
"I know Arsene feels exactly the same way.
"Where we are currently is off the shoulder of the world's top teams.
"I think the best teams in the world are in Europe and you think about the great names in world football like Real Madrid, Barcelona and Bayern Munich - I don't think we're at that level yet but that's where we're aiming to get to
"It's one thing to say that and it's another thing to be able to deliver it."
During Arsenal's long slump without silverware - the move from Highbury to the Emirates Stadium led to straitened times for the Gunners and saw leading players sold rather than retained - it seemed they might struggle to rediscover former glories, despite reaching the Champions League for 17 successive seasons.
"It has been incredibly frustrating not being able to be where we want to be these last few years, so winning the FA Cup was a fantastic moment," Gazidis added.
"(But) I don't come out of that feeling satisfied like we've achieved what we need to achieve
The hunger for success is immediate.
"The moment you get away from that euphoria of the moment, the next question is, 'How do we have more of that?'
"That's what everybody at this club is focused on
There's no satisfaction in it - it's what do we do now."
Where Cesc Fabregas and Robin van Persie are among the players to have departed, now Arsenal are signing the likes of Mesut Ozil and Alexis Sanchez and keeping their most talented players in a sign of their ambition.
"We're signing some fantastic young talent and we're keeping our players now, unlike the situation two or three years ago when we were really financially challenged and were losing our top players," Gazidis added.
"We're signing our top players to long-term contracts
Guys like Jack Wilshere and Aaron Ramsey."
Source : PA