The Gunners manager celebrated 18 years in North London earlier this month, and the Frenchman's work with the team since his arrival has been praised by one of the most powerful members of the club's hierarchy.
"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," Gazidis told the club's official website.
"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."
Wenger signed a three-year contract extension in May.