The Spanish international is set to leave the Nou Camp at the end of the season when his contract expires in search of a new challenge.
It is understood that the 32-year-old has already reached an agreement in principle with Monaco, yet City are still plotting a late swoop.
According to reports, the deal with the Mediterranean side can be overturned if any interested party grants the Ligue 1 giants a compensation payment.
City are believed to be ready to do so, with Manuel Pellegrini unconvinced by current number one Joe Hart.
The England ace was dropped earlier this season on the back of a number of shaky displays, but he has since returned the starting XI.
Yet Pellegrini is ready to axe him from his first-team if he can land Valdes.
The presence of international team-mates such as David Silva and Alvaro Negredo may be key in luring him to the Etihad Stadium, as could the influence of director of football Txiki Begiristain – who previously held a backroom role at Barca.