The French enforcer is set to be a free agent in six months’ time, with his current deal due to expire at the end of the season.
This has alerted a number of top sides, including City.
Despite possessing a wealth of central midfielder options, Manuel Pellegrini is keen to recruit the 26-year-old.
A cut-price January move has been mooted, but PSG may opt to play hardball and let their man play out his contract in the French capital.
Some reports suggest that Matuidi may be offered an extended stay in Paris, but it remains unclear as to whether or not the Qatari-backed side are willing to keep him, or the player himself is prepared to stay.
PSG are expected to once again delve into the transfer market in the coming weeks, with Yohan Cabaye of Newcastle a target.
If the Magpies ace arrives it will plunge Matuidi’s role in the squad into further doubt, with the club already possessing a number of experienced players.