The Premier League club spent almost £150m this summer, but failed in their attempts to replace prolific striker Romelu Lukaku.
Everton were linked with a move for Arsenal's Olivier Giroud and Chelsea's Diego Costa, but neither came to fruition.
Now, 'TuttoMercatoWeb' are reporting that Ronald Koeman is ready to take advantage of the fragile situation at PSG and make a bid for Cavani.
If the Toffees do wrap up a deal for the Uruguayan striker, it is of paramount importance they decide who will be in charge of taking penalties.