Reports emanating from France earlier this week claimed big-spending PSG were set to win the race for Cavani's signature and had even agreed personal terms with the player.
However, Leonardo insists Cavani is not on their list of potential transfer targets.
"Now is not the time to talk about the market," Leonardo told Sky Sport Italia. "But I can say that Cavani is not our objective at this time.
"Do not expect an amazing market from us this year - we've already got them at this team."
Leonardo also played down talk linkin Zlatan Ibrahimovic and Ezequiel Lavezzi back to Italy this summer.
Juventus are thought to be keen on bringing Ibrahimovic back to Turin, while former Napoli hit-man Lavezzi has refused to rule out a move to either AC or Inter Milan.
But Leonardo is adamant both players will remain at the Parc des Princes next season.
"Ibrahimovic and Lavezzi will definitely stay here - 100 per cent," added Leonardo.
Leonardo also went on to reveal that he wants Carlo Ancelotti to remain at the helm next season, but that the Italian's future in the French capital depends on him.
"I want [Coach Carlo] Ancelotti to remain, but that will depend on him," concluded Leonardo.