The 32-year-old’s deal at the Etihad is set to expire in June and he is yet to agree fresh terms with the Citizens.
The uncertain situation has piqued the interest of Barcelona, according to the Sun, as the La Liga club would like to bring him back to Spain.
Aguero left Atletico Madrid for City in the summer of 2011, and he's now the English club’s all-time top scorer with 256 goals.
He's free to agree pre-contract terms with another club after entering the final six months of his contract, and PSG are also said to be interested.
The City striker is thought of as a better fit for the PSG attack than current options Mauro Icardi and Moise Kean, and his signing has been made a priority in the French capital.
Barca star Lionel Messi, who is also out of contract at the end of the season, remains the dream target for PSG and could be partnered with his compatriot in Paris.
But recent losses of €100m amid the coronavirus crisis mean that the French giants could be forced to sell prized asset Kylian Mbappe to Real Madrid in order to stick to Financial Fair Play regulations.
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