The Belgium international signed for the Blues in 2011 before spending three seasons on loan at Atletico Madrid, eventually returning to west London in 2014 to stake his claim as the first-choice goalkeeper at Stamford Bridge.
Courtois was instrumental in Chelsea's march to the Premier League title last season but this term has proved difficult for Antonio Conte's men, with a top-four finish in England increasingly unlikely, given they sit 10 points off fourth with six games remaining.
That means no UEFA Champions League football for the London giants next season, something which has led to suggestions some of the club's biggest stars could look to depart in the off-season.
However, that has reportedly not stopped PSG from pursuing the shot-stopper, with RMC Sport claiming the mega-rich French side have already begun negotiations over a move to Parc des Princes.