Carragher believes the Welshman will be out to show his best form after being disappointed with how his first spell on Merseyside ended after just a year in 2007.
"It's a great signing," the vice-captain told Liverpoolfc.tv. "I kept in contact with him when he first left. The longer it goes the less contact you keep with former players so it'll be great to see him again.
"As a kid he always said he was a Liverpool fan and I think he was quite disappointed with how it finished, with how he left. He'd have liked to have done a lot better and hopefully this gives him the chance to do that.
"I don't know if it's a free transfer or whatever it may be, but for the last few years at Man City he has been excellent, not just as a striker but as a wide player. In the squad we've probably only got Stewart Downing as an out-and-out wide player. I think Craig prefers to play as a striker but he could certainly do that job for us."