Lizarazu reckons his former Les Bleus team-mate Vieira, currently head coach of New York City, is ready to succeed the departing Arsene Wenger at the Emirates.
He said: “When you talk about roots and DNA, it's something important and I think Patrick is ready. He's coaching in New York and I think he's ready.
"Things were getting a bit difficult for him (Wenger) at the end, which has been spoken about. But what you've got to look at, when you're being honest, is a man's work a whole.
"The 22 years he achieved at Arsenal were exceptional.
“He left his mark on the club the way Ferguson did with Manchester United. He was more than a coach, he was a general manager.
"He built a team, he built a club, and few managers have had such an impact on a club the way Arsene Wenger did.
“He had a sense of aestheticism, an attacking way of playing - and an elegance and class. I liked what Mourinho said, because they were always going at each other. It was a real measure of respect.
"It was great to see that and all these big managers who spoke so highly of Arsene. Well done Arsene.
“Personally speaking, he's a very endearing person. I think he will win the Europa League with Arsenal and finish in style.
"Paris Saint-Germain would be fantastic for Paris, but I don't think it would be for Arsene.
"They need someone like him to embody the institution which is Paris Saint-Germain, but after 22 years with Arsenal, I don't think it interests him much."