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.