The Spaniard is out of contract at the end of the season and had a verbal agreement to join the Ligue 1 side on a free transfer in the summer.
But Valdes is believed to have missed the deadline set by Monaco to sign a binding pre-contract, which has angered billionaire owner Dmitry Rybolovlev.
And City are reportedly confident of hijacking the deal in order to put pressure on Joe Hart, who has just regained his first team duties following a poor spell at the beginning of the season.
Manuel Pellegrini has dismissed reports of any interest in Valdes, and refuses to make any comment on him ahead of City’s Champions League meeting with Barcelona at the Nou Camp.
Valdes, 32, has spent his entire career with the Catalan giants but is looking for a new challenge in Europe, with the Premier League an attractive option.
Meanwhile, City will travel to Barcelona for their Champions League last 16 second-leg clash just three days after they play Wigan in their FA Cup quarter-final.