The striker is out of contract with Barcelona next summer and will openly be able to negotiate with other clubs in less than two months' time.
The 33-year-old handed in a transfer request at Barca in August, requesting the club referred to the clause in his contract that allows him to leave for free at the end of every season.
However, the Catalan giants said his 700m euro (£624m) release clause would have to be met and Messi reluctantly stayed put instead of going to court.
Now, per The Telegraph, City could make a move for Messi at the start of 2021 when he is free to hold talks with other clubs.
City were among the clubs linked with Messi when he made clear he wanted to end his 20-year stay at the Nou Camp, nine days after an 8-2 defeat by Bayern Munich in the Champions League quarter-finals.
City's chief operating officer, Omar Berrada, recently stated that Messi is still being considered at the Etihad Stadium after missing out on him in the summer.
"I think any club in the world would like to explore the possibility of him joining their team," he said. "He's probably an exception to potential investments that we'd do."
Messi, of course, worked with City boss Pep Guardiola at Barcelona, winning three La Liga titles and two Champions Leagues during their time together.
Despite the bitter summer wrangling, Messi remains Barca captain and has played every game this season, scoring three goals in his eight matches.
"I thought and was sure that I was free to leave," Messi told Goal in September. "I told the president and, well, the president always said that at the end of the season I could decide if I wanted to go or if I wanted to stay and in the end he did not keep his word.
"Now I am going to continue in the club because the president told me that the only way to leave was to pay the 700m clause, and that this is impossible."
According to Barca sources, Messi's future could become clearer in March when Barcelona's elections for president Josep Bartomeu's successor are held.
If Messi is to leave the Nou Camp, it would end two decades at the club for the Argentinian genius.
Before then, Barcelona face a race against time to avoid bankruptcy and need to trim their wage bill by €190m.
The club have begun negotiations with their players over a 30% wage reduction but terms need to be agreed by Thursday November 5 or bankruptcy in January is possible.
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