The Argentine has been missing from action as a result of injury but Pep Guardiola’s side have missed him.
And he is in the final year of his contract at the Etihad, with Inter Milan looking to snap him up.
They are prepared to offer the former Atletico Madrid star a two-year contract, according to Calcio Mercato.
Inter are desperate to wrestle the Serie A title from Juventus, who have dominated Italian football over the last decade.
Antonio Conte has eyed Premier League talents before, with the likes of Christian Eriksen, Romelu Lukaku and Alexis Sanchez all making the move to the San Siro.
And City could be prepared to let Aguero go without a fight as they make room for Messi.
During the summer, the six-time Ballon d’Or winner came as a close as he has ever come to calling time on his Barcelona career.
Messi has spent his entire professional career at the Nou Camp but a fallout with the board saw him demand an exit.
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City were the most likely suitors, with the money available to afford his wages – as well as the manager.
Guardiola and Messi enjoyed a trophy-laden spell during the coach’s time in charge of Los Cules, including the treble.
But ultimately, a transfer never materialised with the Barca board unprepared to sanction his departure.
However, that decision will be out of their hands next year when Messi’s contract expires.
With the 33-year-old still keen on leaving, any chance of a new deal looks slim at best.
And City chief Oma Berrada has hinted that they could launch an attempt on Messi next year when he becomes a free agent.
He told the Manchester Evening News: “He’s an amazing talent, he’s somebody that can make a significant impact at any club in the world on and off the pitch immediately.
“He’s the best player in the world, he’s the best player of his generation. I think any club in the world would like to explore the possibility of him joining their team.
“The fact that it was commented that he wanted to come to play for City just shows you how far the team has come over the last years where the best talent of his generation and potentially saying he wants to come and play for us.
“It’s hard to guess what could happen. If you think back to those two weeks where everything played out at Barcelona, it’s almost impossible to guess what will happen next summer.