According to the Mirror, Ronaldinho has fallen out of favour at the Rossoneri and it is understood Milan would be willing to let him leave for the right price, despite having two years left on a £6m-a-year deal he signed last summer.
City manager Mark Hughes attempted to sign the Brazilian from Barcelona last summer, but was unsuccessful, and more recently, in January, spectacularly failed in efforts to bring compatriot Kaka to Eastlands.
Ronaldinho away from the San Siro, and their hopes have been boosted by quotes attributed to the player's brother, Roberto de Assis Moreira, who said: "There is no chance of Ronaldinho going back to Brazil at the end of the season.
'But if you ask me whether he could change teams in Europe, I would say yes, definitely."
City have also been linked with a big-money move for Chelsea striker Didier Drogba.
The Sun reports that Hughes made a firm enquiry about the Ivorian in January but was rebuffed. However, it has been suggested Chelsea did tell City that if they came back with another offer at the end of the season, their efforts would prove successful.
The Sun claims City will bid £15m for the 31-year-old and want to push through a three-year, £150,000-a-week deal as soon as the transfer window opens.