French newspaper L'Equipe claims a dispute between Matuidi's agents and the club is threatening to derail fragile contract talks, with the France international open to moving abroad.
He could leave on a free transfer at the end of the season as his current PSG contract is set to expire. But he'd be free to discuss terms with a club like Chelsea or City from January under Bosman regulations.
The report claims Matuidi has not discounted the opportunity to leave PSG, with Chelsea and City the two most likely destinations.
His first-choice remains to stay at the Parc des Princes but if the dispute between club and player ends badly, PSG may lose him for nothing.
Le 10 Sport claims the risk is "real", with Chelsea and City monitoring the situation closely as the January 1st deadline nears.
Matuidi, a France international midfielder, has blossomed into one of Europe's best defensive midfielders since his move from St Etienne to the French capital.