On Friday, Wenger announced that he would end his 22-year reign with the Gunners at the end of the season, with the Frenchman having won three Premier League titles and seven FA Cups.
For a number of months, there has been speculation regarding Wenger's replacement with Carlo Ancelotti, Luis Enrique, Thomas Tuchel and Brendan Rodgers all being linked with a switch to the Emirates Stadium.
However, as it stands, a number of leading bookmakers rate Vieira - currently manager of New York City FC - as the most likely successor to his compatriot.
During his playing career, Vieira was captain of the North London outfit, with 406 appearances being made in all competitions over a nine-year period.
Tuchel and Germany boss Joachim Low are currently considered to be Vieira's biggest challengers for the position.