Quoting several 'respected' sources in Portugal, the newspaper claims City boss Manuel Pellegrini has sanctioned a bid for the Argentina attacker, and that Benfica have already begun the process of replacing him.
The 23-year-old winger is valued at €40m by his club, but Benfica president Luis Filipe Vieira Ferreira could be open to negotiation.
There is an understanding at the Etihad Stadium that the City squad was lacking pace in wide areas last season.
They've already brought in Jesus Navas from Sevilla, and Salvio has been compared to the fleet-footed Spain international.
Salvio has a better goalscoring record though - he managed 10 in 29 league appearances for Benfica last term.
City have been aggressive early in the transfer window so far. Having already clinched deals for Navas and Brazilian midfielder Fernandinho, the club announced the capture of another Spain international, striker Alvaro Negredo, from Sevilla early on Friday morning.
And an agreement with Fiorentina has reportedly been reached for Montenegrin forward Stevan Jovetic, which should give Pellegrini plenty of attacking options following the departures of Carlos Tevez and Mario Balotelli.
Salvio was an ever present for Benfica last season.