The Sunday Express reports that PSG will make a move for Mourinho if his second spell at Stamford Bridge comes to a premature end.
Chelsea have struggled at the start of the season, both on and off the pitch.
The Blues have already lost to Manchester City, Crystal Palace and Everton this season.
Mourinho signed a new four-year contract at Chelsea last month, but reports claim that his job is under threat following their poor start to the season.
PSG’s owners Qatar Sports Investments are reportedly keen to know the future plans of Mourinho, as they believe the former Real Madrid boss could take the club to the next level.