The France international has helped fire the Gunners to the summit of the Premier League so far this season, hitting five goals in 10 appearances.
Consequently Gazidis believes a winter addition is essential if the club are to sustain their title challenge for the remainder of the campaign.
"We will see where Arsenal will be in January and whether or not the club will invest in another forward," Gazidis told L'Equipe
"Olivier Giroud won't be able to go on all alone until the end of the season. We need to buy."
Wenger's men travel to Old Trafford on Sunday for a clash with Manchester United, which is scheduled to kick off at 4pm.