Valdes is out of contract at the end of the season and both he and the La Liga club have decided a new deal would not be beneficial.
The Spanish international has been with the Catalan side since he was a kid, but a new chapter in his career will begin when he decides on a new club at the end of the season.
Despite the recent fine form of number one Joe Hart, Pellegrini is still keen to see what Valdes will offer to the title chasers.
A number of backroom staff and board members at the Etihad have worked closely with Valdes before and so could persuade the ‘keeper that City is the place for him.
Liverpool, Monaco and Napoli are also chasing the stopper who is able to talk to foreign clubs over a summer move in a pre-contract agreement.