The report in Portuguese newspaper A Bola claims the French giants are considering a €40m offer to bring the Stamford Bridge playmaker to Paris in the winter window. Mata has been continually linked with a move away from Chelsea ever since Jose Mourinho returned to the club.
A two-time Chelsea player of the year, Mata has failed to nail down a first-team place under Mourinho.
The Spaniard made only his third Premier League start of the campaign against Norwich on Saturday, but he was withdraw after 81 minutes with the scores still deadlocked at 1-1.
The Blues eventually won the match 3-1, goals from substitutes Willian and Eden Hazard enough to hand Chelsea the three points from the trip to Carrow Road.
Where last season under Rafa Benitez Mata was the centrepiece of the Chelsea attacking unit, under Mourinho he's been often deployed on the right or left.
Mourinho has spoken of the need for Mata to "adapt" to different tactics, and the Spain international has indicated his willingness to keep his head down and work hard to win back his first-team spot at Stamford Bridge.
But the report claims PSG are willing to test Chelsea's, and Mata's, resolve with a €40m offer in the January window.