Corrigan, who now works as a goalkeeping coach at West Brom, wanted to take Hart to the Hawthorns after spotting the youngster's potential at Shrewsbury.
He revealed to the Lancashire Evening Telegraph: "When I first joined West Brom, I discussed Joe with Bryan Robson, who was the manager at the time.
"I went to watch him at Shrewsbury, and was very impressed. I went back to Bryan with a high recommendation, and we tried to get hold of him to bring him to West Brom. But City had already been to see him by then, and we couldn't match the money they were prepared to put down.
Corrigan has been impressed by Hart's level-headed character and mental strength, which he feels are as important a part of a top-class goalkeeper's armoury as ability.
But he adds that it will be a few years before City and England really get to see just how good the youngster can be.
He said: "He's got the potential to be an international goalkeeper, but you have to remember that he's only a young lad. Goalkeepers don't reach their prime until they're in their mid-to-late 20s.
"Look at David James. He's a keeper who is still going strong at 37. Dean Kiely's the same age, and he's proving his quality with us at West Brom. So it will be interesting to see how Joe develops over the next few years.
"Whenever I've heard Joe speak or read things he's said, he has come across as a level-headed character. And that mental strength is a major asset for a goalkeeper.
"But he's got the ability too. He's got quick feet, he's tall, he's a good kicker and he's got good reflexes.
"And he'll get stronger the older he gets. So if he handles the pressure in the right way, you never know what he can achieve."