The Gunners boss has announced that he will leave the north London club at the end of the 2017-18 season following a difficult campaign for the Frenchman.
Arsenal are in sixth place in the Premier League table and 14 points adrift of Tottenham Hotspur in the race to secure a Champions League spot next term.
The Gunners haven’t won the Premier League title since 2003-04 when Bergkamp and Vieira played a key part in their famous unbeaten season.
Wenger’s men missed out on a Champions League spot for the first time under the French coach last season after Liverpool FC finished ahead of the north London outfit.
Former Arsenal midfielder Petit would like to see one of his old team-mates take over the reins from Wenger at the end of the 2017-18 season.
“The hardest decision for the board will be whether to take a big-name, experienced manager or to bring back a legend like Patrick – or Dennis Bergkamp, or Gio van Bronckhorst, for example,” Petit told Paddy Power.
“There are several former Arsenal players who are managers now.
“It’s time for some of my former team-mates to step up and say they’re ready for it.”
Bergkamp worked as a coach at Ajax for six seasons before he was dismissed at the end of 2017.
Van Bronckhorst is currently in charge of Dutch side Feyenoord after leading the Eredivisie side to a fourth-placed finish.
Vieira, meanwhile, is in charge of Major League Soccer outfit New York City FC.
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