Wenger, whose contract at the Emirates Stadium expires at the end of this season, has previously been linked with a move away from the club that he has managed since 1996.
Ligue 1 leaders Paris Saint-Germain were said to be keen on his services prior to the appointment of former France coach Laurent Blanc in the close-season
Arsenal are top of the Premier League going into Tuesday's trip to Southampton, and Gazidis revealed that Wenger is set to be rewarded for a fine season.
"Arsene will be extending (his contract) with us and at right time we will make that announcement," Gazidis said.
Wenger's men are a point clear of Manchester City at the summit of the English top flight after taking 51 points from 22 games, with Chelsea a point further back in third.
Arsenal have not won the Premier League title since their famous unbeaten season in 2003-04, which was the Frenchman's third top-flight crown.
