The 41-year-old is currently in charge of MLS side New York City, who are part of Manchester City's stable of sister clubs across the globe.
The France international also played for City but is best remembered in this country as Wenger's captain and midfield enforcer in an era when Arsenal were always contenders for the Premier League title, and won it three times.
Those days are long gone of course, with Wenger's current crop only able to qualify for next season's Champions League by winning the Europa League, as Manchester United did last season.
Failure to get past Atletico Madrid in the semi-finals will leave Arsenal jostling with Burnley to avoid finishing seventh and therefore beginning next season's unwanted Europa League campaign with qualifiers that would clash with a freshly-announced pre-season tournament in Singapore.
Wenger is approaching the halfway stage of a two-year contract extension that many fans were adamant should not have been handed to the veteran, who has grown used to speculation about his future.
And Wenger did not dismiss Vieira's credentials as his successor, but hinted that a candidate might require more than a spell in America on his CV to land the post.
"He’s a guy who has the potential one day, yes," he said. "I’ve followed his managerial career. I think he does very well. But overall, this Premier League is special, you know.
"There are plenty of former players who played here who have potential and the intelligence and the knowledge to do it. So there’s plenty of choice, don’t worry about that."
Wenger is convinced the Premier League isn't as special as it might be when it comes to decision-making however.
A request for more information on the pros and cons of introducing safe-standing areas in top-flight stadia was a rather lukewarm response in his eyes.
"At the moment, I would say that the Premier League is very conservative in all its decision-making," he said. "You can see that with VAR and you see it as well with standing.
"The Premier League has been created by people who wanted to be in front of everybody else. Overall I must say at the moment we look a little more like we look first what happens everywhere else, then if it goes well we follow it.
"That’s the tendency, always, when you are successful, not to take many risks anymore and 'let’s continue like that'."
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