Vieira is currently regarded as one of the favourites to replace Wenger, and Petit - who spent three years with Arsenal between 1997 and 2000 - has claimed that his French compatriot is keen to secure a high-profile job in Europe.
The 47-year-old told Paddy Power News: "I'm a great friend of Patrick, so perhaps I am biased, but with everything he has done with Manchester City and New York City FC, and the way he is regarded by fans of Arsenal, I would be very happy if Arsenal decided to appoint him as the next manager.
"I don't know if that will happen, but I hope it does for Patrick's sake. I know he wants to come back to Europe to manage a team, and I guarantee that he loves Arsenal very much.
"The last time we spoke together about his future, he was very grateful to be working in the USA, but it's a first step for him. One day he has to manage a big team in Europe or the Premier League - that's what he's working towards, that's what he expects."