City finished 18 points behind champions Liverpool in the Premier League last season and were knocked out of the Champions League in the quarterfinal stage by Olympique Lyon but Pep Guardiola’s men won the Carabao Cup as compensation for an underwhelming campaign.
Messi has made clear his intentions of leaving Barcelona as soon as possible and has been linked with a reunion with former manager Pep Guardiola and close friend Sergio Aguero, who are still employed by Manchester City.
While Carragher believes Messi’s potential arrival in England will bode well for the Premier League, the former England international is adamant the six-time Ballon d’Or winner will not make the Cityzens unbeatable.
"I'd love to see Messi in the Premier League," Carragher told Sky Sports.
"I want to watch him and I want to analyse him and look at him on Monday Night Football. The only place he can really go is Manchester City with the history he's got with the manager and with the financial clout the club have got.
"I don't think Liverpool will go anywhere near that situation from a financial point of view, number one, and also because of the way Liverpool play as well.
"They're a lot more energetic than City, who play a more technical game which would suit Messi a bit more - but how you get that deal across the line I'm not sure. With the figures involved, it's mind-boggling.
"But I want Messi in the Premier League, and if it has to be City, OK - I'll take that one. If someone like Messi moves, there's only two or three clubs he can go to.
"To me, it only looks like PSG or Man City he could end up at really. I want to see him in the Premier League. It would make Man City stronger but it wouldn't make them unbeatable. Barcelona haven't won the Champions League for a few years.
"Liverpool famously knocked Barcelona out of the Champions League a couple of seasons ago so it doesn't mean it's the end for everyone else - it just means it's brilliant to have Messi in the Premier League. Fingers crossed it happens."