Vieira joined Juventus from Arsenal in 2005, but has now moved on to Inter Milan where he has won the Italian title.
He told the Sunday Mirror: “Bar Sir Alex Ferguson, there isn’t another manager out there who knows and understands English football better than Arsene.
“It would be fantastic for the England team if he became coach because he knows the game and the players.
“I say that because I don’t know what the future is for Arsenal after losing David Dein. That was a very hard blow for the club and the big question for them now is what Arsene will do.
“He has always said he will not break his contract, but he was so close to David. Arsene has achieved big things over the past 10 years, but David played a very big part in that success. Arsene has shown that he doesn’t need a lot of money to be a success, but it was vital to him to have someone to work closely with – and that was David Dein.
“Now he hasn’t got that security there is a question mark over his head.”