There had been reports that the Ligue 1 leaders had agreed a deal for the Napoli star but the Brazilian has moved to dismiss such speculation
The Ligue 1 leaders are one of several sides to have been linked with a summer bid for the Napoli forward, who has refused to commit himself to the Partenopei beyond the end of the season.
However, Leonardo is adamant that there will be no approach from PSG for Cavani, this season's top scorer in Serie A.
"The Uruguayan is not our goal this summer," the Brazilian told Sky Sport Italia. "You should not expect a sensational transfer market [from PSG] because we already have champions."
Leonardo, who has been linked with a return to Inter of late, was just as definitive when it came to discussing his own future in the French capital, as well as the possible departures of Ibrahimovic and Ezequiel Lavezzi.
"I will stay in Paris next year in the same way as Ibrahimovic and Lavezzi," the former AC Milan star added.
"I have a good relationship with [Inter president Massimo] Moratti, but I don't have the intention of returning to Italy.
"If there are many teams interested in them [Ibrahimovic and Lavezzi], it just means that we had a good transfer market last summer!"
Leonardo added that Carlo Ancelotti will only leave the club if he wants to.
"We want him to stay, but his future is in his own hands," he revealed.
PSG are currently nine points clear at the summit of Ligue 1 with just five rounds remaining.