Reports have suggested that Vieira and Arteta, both ex-Arsenal midfielders, are on a five-man shortlist alongside Juventus boss Massimiliano Allegri.
Vieira has enjoyed success as coach of MLS franchise New York City since being appointed to his first senior role in 2016 and recently said he was “ready to coach any side in Europe.”
But Petit, who formed a formidable midfield partnership with Vieira in the late 1990s, told RMC he felt it was too early for him to take the job at the Emirates Stadium.
“For me, Allegri has done remarkable work at Juve with a budget far from that of the big European teams,” he said.
“Vieira could also be a solution, but I think it’s still premature.”
Arteta, now on Pep Guardiola’s coaching staff at Manchester City, has been put forward as a candidate as a result of his work with the Premier League champions.
But Petit, who won the Double with Arsenal in 1997/98, said: “I don’t see it. He’s very good next to Pep Guardiola on the bench at Manchester City.”