The French club look set to rival the Stamford Bridge outfit for the signature of the 26-year-old, who was Serie A's top scorer last season with 29 goals, with Sky sources learning a £43million offer had been made by PSG.
Sky sources also understand that Jose Mourinho's Premier League side made an approach to Napoli earlier on Tuesday, but are unwilling to meet the £54m buy-out clause in Cavani's contract.
With the in-demand striker keen to end uncertainty over his future, it is believed that talks between his agent and Napoli officials over his fee are due to take place this week.
However, club president Aurelio De Laurentiis is refusing to budge on his valuation, and also denied received a firm bid from the Ligue 1 outfit.
He told Sky Sports News: "We have not had a direct offer from PSG. Napoli is a very rich club and we comply with financial fair play. We don't need to sell any of our players.
"If someone wants to buy Cavani, they must pay 63million euros, net. Not one euro less than 63million euros.
"Otherwise we will be happy to keep Cavani, he has a contract until 2017."
Speaking after Uruguay's Confederations Cup defeat to Italy, Cavani said: "I want to talk as soon as possible with president De Laurentiis.
"We must clear this (situation up) ourselves. I'll talk with him, as it's done between men, really soon.
"Right now, I'm at Napoli and I'm very proud to be there. If I leave one day, I'll be ready to move to a bigger club. We'll see."
Napoli coach, and former interim Chelsea manager, Rafa Benitez reiterated his stance last week that he wants Cavani to stay.
Benitez told Corriere dello Sport: "We want Cavani to stay at Napoli.
"We would be really happy if that's how it works out. If he leaves, then it would only be because someone has matched the release clause or comes up with an irresistible offer.
"Cavani knows how much he is loved and how valuable he is to the city and to the team."