This morning's back pages seem to think so, after the Argentina genius had an alleged fall-out with Barcelona Director of Football Eric Abidal.
Of course, we've been here many times before and Messi leaving Barca has always seemed unlikely - but if he did, would City be his likeliest destination?
Pep Guardiola has always insisted Messi will never leave the Camp Nou - and he may be correct - but the media believe City's many Catalan and Argentina connections mean the Etihad would be a logical destination for the world's greatest player...
Pete Jenson writes: "Messi has a contract until 2021 at Barcelona but with a clause that means he can leave for nothing at the end of the season if he is unhappy.
"The very public row between the two men has left Barcelona sweating on Messi’s commitment beyond the summer and City have always been the club most likely to sign him should he ever move to England.
"But they are not optimistic his social media spat with Abidal over the insinuation that the players got previous coach Ernesto Valverde the sack, changes much.
"Messi, 32, is more likely to use his contractual freedom to his benefit, with presidential elections probable in the summer and candidates going out of their way to make changes that will keep him at the club"
Luis Mazariegos writes: "Lionel Messi can leave Barcelona for free starting next summer, according to a new report. Previously, the signing was practically impossible as he had a release clause of 700 million euro. Next summer, anyone can make a phone call, provided they can pay him 50 million in net salary and convince him to join, according to rumour.
"The news comes at a time when Messi’s conflict with technical secretary and ex-teammate Éric Abidal has dominated news. The Argentine was publicly upset at Abidal’s statement that some players did not work hard during the reign of Ernesto Valverde, Barcelona’s former manager.
"Manchester City feel that if Messi did leave Barcelona, they’d be first in the queue to get him, according to the Manchester Evening News. City have a couple of executives that are old acquaintances of the #10 in Ferran Soriano and Txiki Begiristain. They also have perhaps Messi’s best friend on the football pitch, Sergio Agüero, and Messi’s favorite coach, Pep Guardiola."
Rob Dawson reports: "Manchester City are monitoring Lionel Messi's public fall-out with Barcelona and believe they would be in the running if the Argentina star decides to leave Camp Nou, sources have told ESPN.
"Messi has been involved in a row with Barcelona sporting director Eric Abidal over his claims players forced the dismissal of coach Ernesto Valverde.
"The 32-year-old reportedly has a clause in his contract that would allow him to leave the club for free at the end of the season, although it is unclear whether he could join a Champions League rival like Manchester City. The Premier League holders privately admit his departure remains unlikely, but they would be interested if he decides to move either this summer or at the end of his current deal in 2021."
Daniel Blackham writes: "Manchester United haven’t had an easy time of it regarding transfers recently, and could be set for new heartache, as they could miss out on another transfer target to rivals Manchester City. United made two signings during the January transfer window but missed out on top target Erling Braut Haaland.
"United were believed to be keen on signing Jude Bellingham during January before loaning him back to the Blues for the second-half of the season.
"However, they were unable to agree a deal with Birmingham, and the player stayed put.
"The Premier League outfit reportedly bid £25m to sign him, but Birmingham held out for more.
"Now, they could be set to receive the fee they want, with The Sun claiming back-to-back Premier League champions Manchester City ready to enter the arms race.
"United are unlikely to be able to offer Bellingham the prospect of Champions League football, whereas City will.
"The Citizens aren’t the only team preparing to take advantage of United’s failure to make a deal in January."
That's all for this morning's Media Watch - but stay with us throughout the day as we bring you all the latest City news.