The Frech broadcasters claim Man City owner Khaldoon Al Mubarak could trigger the Argentinean's € 300 million release clause by the end of the current summer transfer window.
Messi agreed a new deal until 2021 last month, but the five-time Ballon d'Or victor is yet to officially put pen to paper.
Messi has scored 508 goals in 585 games for Barcelona since 2004, helping the La Liga giants win eight titles and the Champions League four times and emerge as one of the greatest players of all-time.
The five-time Ballon d'Or victor agreed a new deal with the Catalan giants last month, but he has yet to put pen-to-paper, leading to suggestions he could still leave the Nou Camp. Meantime, the blaugrana must deal with another threat after the departure of Neymar.
Barcelona are struggling in their attempts to sign a replacement, with Liverpool adamant Philippe Coutinho will not be sold, while on the pitch Messi has seen his side fall to successive defeats to Real Madrid in the Super Cup.
Messi would demand a starting spot under City manager Pep Guardiola, with whom he worked during the pair's time together at Barcelona, and would add to an already exciting forward line. This rumour has gathered pace after Manchester City chairman, Sheikh Mansour reportedly told the fans that the club is working on a world record deal this summer.
Boston Free Speech Rally and Counter-Protests LIVE STREAM
The news organization noted that just eight people were arrested out of the tens of thousands who gathered in the city. President Donald Trump applauded the people in Boston who he said were "speaking out" against bigotry and hate.
NC team notches ideal game in Little League World Series
Rancho Santa Margarita, Calif., representing the West, walked away with a 10-1 win against Walla Walla, Wash., from the Northwest. That put the pressure on Carson Hardee to close it out, and close it out he did with the team's tenth strikeout of the game.