The newspaper claims that the 30-year-old can "no longer stay with the French side" with Juventus ready to bring the former Napoli player back to Serie A.
Cavani reportedly fell out with Neymar once again on Wednesday night after the Brazilian, who had already scored three goals, decided not to give his team-mate the chance to become the club's leading top goalscorer from the penalty stop, choosing to take it himself.
The Uruguayan still has two years left on his current contract so the Italian side may have to spend big to tempt PSG, who could be reluctant to sell their prolific striker.
Cavani has an impressive record at the Parc des Princes, netting 108 times in 153 appearances, which equates to a goal every 1.4 games.