Fellow England internationals James Milner and Gareth Barry both believe Hart would be the ideal candidate to take up the armband going into the Euro 2012 finals.
Their support comes following last week's decision by the Football Association to strip John Terry of the captaincy, an issue that ultimately led to Fabio Capello's departure as manager.
Although the FA have yet to appoint a new manager, Milner and Barry feel any new man should consider Hart for the skipper's role.
Although Hart is only 24 and seemingly lacking the experience of other candidates, Barry said: "I'd give it to Joe, my friend.
"Harty has been fantastic all season. It wasn't just against Villa (yesterday) that he's made a world-class save, he's done it in a few games.
"That is why he is being talked about as one of the best in the world."
Milner also feels Hart could fulfil the role.
He added: "It's nothing to do with me in terms of the decision.
"But he is a great character, he talks, he is not afraid to say what he thinks.
"I'm sure he is going to be England's number one for a long time, so he is as good a candidate (for captain) as anyone."
As to Hart's talent, Milner added: "He has been absolutely unbelievable for us this season.
"He's a world-class goalkeeper, definitely one of the best I've played with, and he is going to get better and better as well."
City were indebted to Hart for producing a wonderful reaction save to deny Darren Bent in injury time to give them a 1-0 win at Aston Villa that sent them back to the top of the Barclays Premier League.
After a run of just one victory in their previous six away games, the result was a crucial one for manager Roberto Mancini's side.
Barry said: "We played some great stuff early this season, winning games by scoring three, four goals. Now it's all about the three points.
"We've had a few scrappy games like this recently where we haven't managed to get three points, and even lost them, so it's all about the win.
"At this stage of the season any away game is going to be tough, so it was a massive three points for us.
"The away form has also been a bit up and down. People had started questioning it, so it was important to put that to bed with a win, and we did that well."
With 13 games to go and the title on the line, Milner also knows it is not how you win that counts, but simply that you do win.
"Three points is three points, and that's the main thing," said Milner.
"We played well against Villa, and probably didn't score as many as we should have done, but that's how the season goes.
"You have suspensions, we've had a lot out recently, injuries as well, players away at the African Nations Cup, which is what football is all about and when your squad gets tested.
"So if you can keep picking up points when you're missing players then that is obviously a positive."