Vieira has been talked about as a potential replacement for Arsene Wenger, having spent nine years at the club in his playing days.
"I'm sure [the press] will know before I do," Vieira said.
"Of course [it's an honour to be linked], because you're talking about Arsenal Football Club, and it's a big football club, it's an honour, but I have never been in touch.
"I know how committed Wenger is to this football club, and it's not easy to go through what he went through.
"You know that you will have a [tough] time during the season, where one day you are the best coach and the next day you will be the worst.
"It's all about, I believe, how you can be consistent in yourself, in how you have to be consistent with the media, with the fans, with your players.
“I think it's not about having this rollercoaster where when you are doing well you are [up] there and when you are down ... no, it's about being consistent."