The England midfielder signed for Manchester United for ?17 million from Bayern Munich in 2007, but made just 39 appearances for Sir Alex Ferguson's side over four seasons as he battled persistent knee problems.
Eventually, United lost patience and released Hargreaves, who took to posting a video on the YouTube site to demonstrate his fitness, having travelled the world to receive treatment on his knee.
Lescott and Hart are both currently with the England squad as they prepare for Friday's Euro 2012 qualifier away to Bulgaria.
But the pair, speaking on the eve of the closure of the transfer window, were excited by the prospect of Hargreaves joining them at Eastlands.
"Owen is an experienced player, he has played in the Champions League, is an international," Lescott told reporters at England's hotel on Tuesday. "It is only going to be good for the City squad if he signs.
"I've worked with Owen at England level and he is a great professional.
"People ask if it represents a gamble but the club know what they are doing, Owen knows what he is doing. He is still a good player.
"He hasn't played as much as he would have liked over the last couple of seasons but the medical team we have is very good and very strong.
"If we can get him fit, I'm sure it won't be very long before he is back to his best. He will be a player with a point to prove after his injuries."
England goalkeeper Hart added: "It would be a good signing. Obviously, Owen Hargreaves has done great for Bayern Munich.
"He has struggled a bit since he came to Manchester United but that is not down to ability, just his fitness.
"If he can get himself fit and does sign for Manchester City, it can only be a positive.
"He was a very important England player. If he can get back to that form, obviously he would be an asset."
Hargreaves was voted England's best player of the 2006 World Cup in Germany and signed for United a year later.
He played in the 2008 Champions League final victory over Chelsea in Moscow but then began to suffer with knee problems, restricting him to four appearances in three seasons.
Hargreaves lasted just 10 minutes of his comeback against Wolves last September and Ferguson consequently decided against renewing his contract with the English champions.
But former Old Trafford team-mate and England striker Wayne Rooney said it would be good to see Hargreaves resume his career.
"I wish him luck and I hope he gets back," Rooney told the England press conference. "Everyone knows that when he's fully fit he's a great player, he's a different type of midfielder to what we've had in England.
"We all hope as England players and fans that he can one day get back to his best."
Source: AFP
Source: AFP