The Chile international, who has shared first-team duties with German Marc-Andre ter Stegen since joining the Spanish giants in 2014, has been given the green light to join the Citizens by Barca.
This after the Spanish club reportedly sealed a deal for Ajax Amsterdam keeper Jasper Cillessen.
It has been suggested that the fee is worth around £17m, with the promise of regular first-team minutes said to be a crucial factor in convincing him to swap the Nou Camp for the Etihad Stadium.
In his two seasons with the Blaugrana, Bravo has made 72 appearances, almost exclusively in the Primera Division, while Ter Stegen has donned the gloves in the club's cup games.
The news of Bravo's imminent arrival will in all likelihood expedite the departure of City's out-of-favour goalkeeper, Joe Hart, with City boss Pep Guardiola last week informing the England international that his first-team opportunities would be limited in the coming campaign.
Hart is not short on suitors, however, as Everton, Sevilla and Borussia Dortmund have all expressed an interest in acquiring the gloveman's services.
The 29-year-old has not featured under Guardiola this season, with Willy Caballero preferred between the sticks for the club's first three games of the new campaign.