The Express reports that the French giants prepare a move for the Dane before the European transfer window shuts on August 31.
Eriksen is yet to sign a new contract at Tottenham, but talks are ongoing.
PSG have long been linked with a move for Eriksen, but Spurs are desperate for the 26-year-old to stay at the club.
Eriksen has two years left on his current contract with Tottenham.
The highly-rated midfielder has also been linked with Spanish giants Real Madrid.