In recent weeks, there have been more calls for Wenger to step down from his position at the Emirates Stadium, and a number of possible replacements have already been suggested in the media.
Should the managerial job at Arsenal become vacant, Vieira would likely come into contention, but the Frenchman has stressed that he wants to show respect to his former boss when it comes to speculation regarding the position.
The 41-year-old told L'Equipe: "I think that if it is the end of the story, he'll be the first to see it, and I would like to add that given all he has done for the club, what he has built and what he has won, he has sufficient legitimacy to decide himself when he should step down. He has the right to take that decision himself.
"Let's say that, one day, it could interest me. But one day. I can't say any more because there is nothing to say about it and I certainly do not want to upset Arsene, who I adore and for whom I have a lot of respect."
Since January 2016, Vieira has been in charge of MLS side New York City FC.