The 64-year-old's current deal expires at the end of the season and negotiations have been going on for some time to tie up Wenger's long-term future, with the club currently top of the Barclays Premier League.
Wenger continues to play down the concern when pressed on the issue by the media, but last month indicated he had made a decision.
Gazidis also indicated there was no panic over time frames when speaking at the launch of Arsenal's new long-term partnership with Puma, which will see the company become the club's official kit suppliers from July 2014.
"We have always been completely behind him. We are comfortable in the position and relaxed about it. Arsene will be extending with us and at the right time we will make that announcement," Gazidis told the news conference.
Although no official figures were confirmed on Monday, the commercial deal has been described as ''the biggest deal in Puma and Arsenal's history''.
The Gunners are understood to receive around £30million a year from main sponsors Emirates Airlines, and it has been reported the new deal will be for a similar amount when Puma takes over from Nike, who Arsenal have partnered since 1994.
Arsenal smashed their transfer record in the last window with the £42million signing of German playmaker Mesut Ozil from Real Madrid.
It has been reported the Gunners are keen to bring in Ozil's compatriot Julian Draxler from Schalke, although Wenger continues to play down suggestions another big money deal can be completed ahead of the January 31 deadline.
Gazidis indicated significant funds were still available, although those from the new kit deal would not be added to Wenger's warchest until the summer.
"The new partnership represents the biggest commercial deal in Puma's and Arsenal's history," the Arsenal chief executive continued at Monday's news conference.
"The money from this deal will be available to the club from this summer. It represents an important step in our progression on and off the pitch.
"One of our long-term goals has been to increase commercial revenues and there is a football reason for that - from the summer onwards the money will be available for the manager to spend how he sees fit.
"We have a vision to be competing at the top of the world's game, but we don't get there overnight.
"We are doing it our way, without relying on any single individual, on an independent path.
"When we achieve success it will mean so much to everyone that has been in this journey, so let's get there as soon as possible."
Gazidis told Sky Sports News there was no reason to think Wenger would not stay on at the club he has managed for almost 20 years.
He said: "This football club is the football club of his life.
"We are very convinced, and at the right time we will quietly make an announcement that he is the right person to see us forwards."