Pogba's contract at Manchester United expires this summer and there are no indications that he will extend his stay at Old Trafford.
Initially, Pogba was tipped to rejoin former club Juventus or Paris Saint Germain as a free agent but recent reports have included Manchester City in the conversation.
Carragher however does not think Pogba has the right work ethic to succeed in a Pep Guardiola team after watching the champions smash Newcastle United 5-0 over the weekend.
"I wouldn't go anywhere near him," the former Liverpool defender said on Sky Sports. "[City] win the league every year, get 95-100 points every year. He doesn't work hard enough, as much as the other [City] players.
"If Pep could get it out of him, fantastic, there's no doubting his ability... but when you see the players City have, you see [Phil] Foden, Bernardo Silva, these types of players who are brilliant players and don't stop running, don't stop working from minute one to minute 90. That's what makes Manchester City what they are."
Carragher's colleague at Sky Sports, Jamie Redknapp, however is of the opinion that a potential move will be brilliant for both parties.
"An incredible move, it'd be one that, I have to be honest, I wouldn't have seen coming," he said. "But you have to weigh it up. Free transfer, he'll have a point to prove because he's taken a lot of stick since he's been at United.
"No matter what you say about Paul Pogba, as 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'd be a brave move, but I'd love to see that in the Premier League. I think it'd make sense all round."
