The 'Gunners' currently sit at a crossroads, facing the unfamiliar situation of needing to appoint a new manager for the first time in 22 years.
According to 'Sky Sports News', Gazidis, who will have a big say in naming Wenger's successor, believes that Arteta has the credentials for the role, despite his lack of experience.
Former Arsenal skipper Arteta, who enjoyed a fruitful five-year spell with Arsenal at the end of his career and is now making a name for himself as a coach with Manchester City.
The club are thought to have already begun their search for a new boss, with former Barcelona manager Luis Enrique considered by many to be the favourite for the role.
Other names in the frame include Julian Nagelsmann and Domenico Tedesco, but with Arteta having already demonstrated his ability to lead during his period as Arsenal's club captain and with his knowledge of the club he could well be a dark horse for the post.