Vieira was an influential figure in the Arsenal side that won three titles between 1998 and 2004, as well as the Inter team that won four successive Scudetti from 2007 to 2010.
The former France captain currently manages City's Under-21 team, having held several backroom roles at the Etihad Stadium since retiring from playing in 2011.
City currently lie fourth in the table, six points behind leaders Chelsea but with three games in hand, and Vieira says now is the time for the club's "leaders" to stand up and be counted.
"If you want to win the title, you need your leaders to be at their best, on and off the field," he told The Manchester Evening News.
"When you look at our first team, there are so many strong characters, and so many leaders.
"There are different ways of being a leader - some are leaders on the field, and some outside of it.
"But as a team, the way we performed at Hull City (last weekend's 2-0 win) was a strong message, because to get a red card after 10 minutes and still win showed we are really strong.
"It was not just about character but the way we dictated the game, controlled it, that was fantastic. That game showed a really strong message."
Vieira also hailed David Silva - influential in the win at Hull - for his performances, claiming that the Spaniard is one who is already leading by example on the field.
"Since he joined the football club, I don’t think we have really said enough how good he is," the Frenchman added. "He is one of the best players in the world, no doubt about it. For me he is up there.
"When you talk about (Lionel) Messi and (Cristiano) Ronaldo, yes they are fantastic, but David can be put in the same category of players who could play in any team around the world.
"His football brain, his ability to control the ball and play football, is unbelievable. I am a huge fan.
"When the team is struggling, that is when the leaders come out, and David showed he is a leader.
"He may be very quiet but when he is on the field, he takes the responsibility, and that is the kind of leader you need in your team."
