The Frenchman is currently a coach at Manchester City.
Newcastle United's hunt for a new manager looks to be under way, with a big mover in the betting markets emerging yesterday.
The former Arsenal captain is out of contract at City this summer and is believed to be keen on a future in full club management.
His odds have tumbled down to 6/1 to make him the third favourite to get the Newcastle United job ahead of candidates such as David Moyes, Roberto Di Matteo and Michael Laudrup.
Vieira may have no experience in the hotseat but he has revamped the City youth system in recent times and his French background could also be a real winning attribute. The Newcastle squad is packed full of Francophones and Vieira could certainly help to cross that dressing room divide.
It would be a gamble from Newcastle United but, it looks like punters are already doing the gambling themselves.
Maybe the hierarchy at St James Park should do the same.