The 41-year-old, who spent nine successful years in North London during his playing days, is currently learning his managerial trade with New York City FC in Major League Soccer.
A number of former Arsenal players have tipped Vieira to leave his role Stateside and replace Arsene Wenger at the Emirates Stadium, with the bookies placing him among the favourites for the position.
Pires is the latest to talk up his compatriot's job prospects, telling beIN Sports: "Right now, to be manager of Arsenal if we talk about Patrick Vieira of course he is my friend we talk a lot and I can reply yes of course because I think he is ready.
"He has done very well with New York City for three seasons. He has a lot of quality and has the capacity to be Arsenal manager. I don't know what will happen during the summer but I think Arsenal and Vieira should be good together.
"I can imagine him in the dressing room giving advice to the players now he is a manager he is not a player. That's why he is doing very well with New York City. I think he is ready for Arsenal 100%. I hope he will say 'yes I am coming to take your seat on the bench'."
Vieira has welcomed links to the job, admitting that it is an "honour to be mentioned with Arsenal".