Media reports in England have linked Pogba to City on a free transfer, as his Manchester United contract expires this summer.
While Redknapp stated that such a move would be smart by City, Carragher believes they should steer clear of the French midfielder.
"It would be an incredible move," Redknapp said on Sky Sports.
"It would be one I wouldn't have seen coming. You have to weigh it up. On a free transfer, he'd have a point to prove because he's taken a lot of stick at United.
"There's a few times I've watched games between United and City and he [Guardiola] always goes over to have a bit of dialogue. He obviously respects him as a player, there was talk a few years ago that he might have gone for him.
"No matter what you say about Paul Pogba, it's a free transfer - high wages of course but that's not a problem for Man City – you would take him in a heartbeat. He adds a lot to this team and I think he'd be hungry to come and show what he can do.
"He lives in the area, I think it would be an incredible move. It would be a brave move, but I'd love to see that in the Premier League. I think it would make sense all round.
"He would have to be completely different to the player we've seen at United, that's a fact. He'd have to play a lot more like he does for France. I think it's a no-brainer. He scores goals, he adds so much to the team."
Carragher, however, disagreed: "I wouldn't go anywhere near him.
"You win the league every year, you get 95 to 100 points every year. He doesn't work hard enough as the other players. If Pep could get it out of him fantastic, there's no doubt there's ability – no one has ever doubted it.
"But when you see the creative players City have, Foden, Bernardo Silva. These type of players who are brilliant players and don't stop running, working from minute one. That's what makes Manchester City what they are, they're a great team, brilliant manager. I'm not doubting his quality, but he does not work hard enough.
"When you see him in a France shirt or at times for Manchester United, unbelievable quality. Does special things at different times. But we're still six years in and we're still talking about his best position, who can get the best out of him."
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