Torres, 21, has been heavily linked with a return to Spain in recent weeks, with one report claiming that the forward is closing in on a move to the Catalan club in 2022.
According to the Daily Mirror, there are good relations between both Barcelona and Man City, which could help accelerate any potential transfer for Torres, however, the Citizens are still reluctant to let the youngster leave.
The report adds that City are aware of Torres's desire to move back to his homeland but are only prepared to see him depart if they can acquire one of Barca's star players in exchange.
Fati and Pedri, meanwhile, are two more Barcelona talents who City have been monitoring for some time, however both players have recently signed new long-term contracts which include €1bn (£850m) release clauses, making any potential arrival at the Etihad for either player more challenging.
Torres, who has over three years remaining on his contract with Man City, has registered 20 goal contributions in 43 appearances across all competitions since arriving from Valencia in August 2020.