The Gunners are on the lookout for a new manager after Wenger confirmed that he will stand as manager at the end of the current campaign.
Arsenal have regressed under the 68-year-old over the past decade or so and the Gunners haven’t won the Premier League title since 2003-04.
The north London side are in sixth place and set to miss out on a top-four finish for the second successive season under Wenger.
Arsenal lost 2-1 to Atletico Madrid over two legs in the Europa League semi-final following Diego Costa’s winner at Wanda Metropolitano on Thursday night.
The Gunners lost 3-0 to Premier League champions Manchester City in the League Cup final at Wembley back in February.
Former Arsenal midfielder Pires, who was part of Wenger’s title-winning team in 2003-04, wants to see his compatriot Vieira take over the reins from the Frenchman head coach.
“I would like to see Patrick Vieira be given a chance at Arsenal, but I don’t think Mikel Arteta is ready,” Pires told bwin.
“Vieira is doing a great job with New York City so he has an advantage over Arteta who is learning a lot from [Pep] Guardiola as his assistant, but doesn’t have the pressure of being manager.
“Arteta is a good coach but it’s important he proves himself as a manager before coming to Arsenal. I would like to see the new manager keep with the Arsenal tradition of having an ex-player as his assistant. The club has had Pat Rice and Steve Bould and I hope that continues.”
Vieira has been in charge of New York City FC following a stint as a coach at Manchester City.
The Gunners have reached the Champions League quarter-finals since 2010.
Arsenal signed Borussia Dortmund striker Pierre-Emerick Aubameyang and Manchester United midfielder Henrikh Mkhitaryan in the January transfer window.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news