Before taking charge of New York City FC, Vieira coached the City U23s.
Given told the Daily Mail: "I do see him being a manager one day, if Pep steps away in a few years, he would be the perfect replacement. He is such a huge character,' says Given.
"I'm sure Patrick has seen what his team-mate Zidane has done at Real Madrid, won two Champions Leagues in a row. If not City, he'll manage a big club in the Premier League or the Champions League.
"I could tell from his team talks as a player that this guy was going places. We have some big stars in that dressing-room but everything was silent when he spoke, every word was listened to."