The Daily Star Sundayclaim Mourinho's relationship with the club's hierarchy has come under pressure after incidents on and off the pitch.
Despite penning a new four-year contract earlier this month, it is reported he has been in a "fiery mood" during training.
The fall-out with club doctors Eva Carneiro and Jon Fearn hasn't helped and the Blues boss is also thought to be unhappy with his side's performance in their 2-2 draw with Swansea.
Jose Mourinho lost his temper with medical staff and is reportedly unsettled at Chelsea
PSG are understood to be lining up a swoop should his position at Stamford Bridge become untenable and believe next summer could be the ideal time for an approach.
With quality additions brought in thanks to Cristiano Ronaldo's agent Jorge Mendes, the French giants think they have a good chance in the Champions League.
Reports also suggest the club are willing to asses how current boss Laurent Blanc fares in the current campaign before making any decision.
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