The former French Gunner has been linked with the vacant position at the Emirates but Vieira, now head coach of MLS side New York City FC, has apparently been left "disappointed" after being contacted by Arsenal.
One of them, according to France Football journalist Nabil Djellit a few days ago, was a "major role" at Saint-Etienne in France, with Jérôme de Bontin, the man trying to buy the Ligue 1 club, contacting the Arsenal manager directly about it.
In 2018 the team has got off to another solid start.
There have been rumblings that Wenger could be waiting for the France job after the 2018 World Cup, but that all depends on Didier Deschamps' performance in Russian Federation, as his contract was renewed a year ago until 2020. "If the question is, if I'm ready", he was asked by Goal (h/t Sky Sports).
Arteta spent five years as an Arsenal player at the end of his career, making 149 appearances for the club across all competitions.
The north London club have not lifted the Premier League trophy since their famous unbeaten triumph in the 2003-04 campaign.
It appears as though Arsenal are going down a different route this time, although Vieira's association with the capital club means it wouldn't be a surprise to see him take charge at the Emirates at some point in the future.