Freddie Ljungberg, a former team-mate of Vieira's at Arsenal, is currently in temporary charge of the Gunners following the dismissal of Unai Emery. Arsenal are in a terrible run of form, having gone nine games in all competitions without a win.
Vieira has been mentioned as a possible candidate to take over at the Emirates Stadium and has said he would have to consider an approach from the Premier League side if it arrived, per Canal Plus (h/t Robin Bairner of Goal).
"You can never ignore a club where you've spent nine years," said the 43-year-old. "But, honestly, I'm focused on this project at Nice, I feel very good here. It's a very exciting project. I've always said that I'm very happy in Nice. We're all working to move the club forward and there is potential."
While Vieira was speaking after his team beat Metz 4-1, overall it's been a challenging season for Nice. Despite some big investment in the summer, they sit in 11th place in Ligue 1 after their win on Saturday.
As French football writer Jeremy Smith relayed, Nice are capable of scoring fine goals, albeit they lack consistency:
Jeremy Smith @jeremysmith98
Rumours growing that Vieira is now the leading candidate for the Arsenal role. His Nice team scored this brilliant goal at the weekend. But this has very, very much not been the norm during his tenure. Tonight's 4-1 defeat more indicative of how this season has been going. https://t.co/aDelOdNbO4
Get French Football News praised the work the former midfielder did last season with the club, steering them to seventh place in the table:
Get French Football News @GFFN
A steadfast defence, led by cat-like Walter Benitez & €4m summer centre-back signing Christophe Hérelle, made Nice the strongest defensive team aside from Reims. Youcef Atal meanwhile, sometimes from right-back, sometimes from left-wing, constantly made the difference in attack.
With the Gunners, he was an inspirational leader and midfielder. Vieira was at the heart of Arsene Wenger's awesome Arsenal team, winning three Premier League titles, including the 2003-04 prize in which the side memorably went unbeaten all season.
At the moment, the current Gunners side would benefit from some of Vieira's qualities, as they have been devoid of many positive attributes in their disappointing recent run. On Thursday, they were beaten 2-1 at home by Brighton & Hove Albion; James McNicholas of The Athletic lamented a team that has lost its way:
Per Charles Watts of Goal, in recent matches, Arsenal have been dominated by modest opposition:
Whoever takes over at the north London club will have a lot work to do, as there are issues to resolve in all facets of the Arsenal XI.
Although Vieira is adored at the Gunners and would no doubt receive plenty of backing from supporters, he still has plenty to learn about management. At this juncture, Arsenal would surely benefit from a coach who has a lot more experience at the highest level.