But the forward appears to be nearing the Parc des Princes exit after Leonardo gave an explosive interview.
"Neymar can leave PSG, if there is an offer that suits everyone," he told Le Parisien.
"But to date, we do not know if anyone wants to buy him or at what price. All this is not done in a day, that's for sure...
"PSG want to rely on players who want to stay and build something big. We do not need players who would do the club a favour by staying here.
"I do not know a club that has won over time with a player stronger than them. For a club to move forward, it must have control over everything, including on its most important players."
PSG sporting director Leonardo: “Neymar can leave if an offer arrives that suits everybody. We have not received an offer. What is true is that there has been very superficial contact (with Barcelona).” #FCB #Barca https://t.co/4TuzpxIrcg— Jonathan Johnson (@Jon_LeGossip) July 8, 2019
Leonardo confirmed Neymar wants to leave PSG but denied the club could have done more to keep the star forward happy.
"It does not only happen to PSG. There are similar cases in other clubs," he said, using Paul Pogba's situation at Manchester United as an example. "We hear everywhere, in Manchester or elsewhere, that players want to leave their club.
"It also happens at PSG, it's normal. But why should it be considered as a disgrace, as if the club had failed to convince the player to stay, as if it was always the club's fault?
"And in the case of Neymar, who is late for the resumption of training, it will still be the responsibility of the club who has not managed this problem? No. If the player arrives late, it's his fault. Afterwards, there are internal procedures and we will see how things go.
"Players who do not show up the day of the recovery, it happens elsewhere than PSG. We have not received any offers. But we had, it's true, very superficial contacts."
And Leonardo confirmed there have been initial talks between Barca and PSG over Neymar but suggested the LaLiga champions were not seriously interested in signing the 27-year-old.
"They said they wanted to buy but we were not sellers," Leonardo added. "He [Bartomeu] is the one saying it... But we did not see that Barcelona was really in a buyer position.
"You have to talk and negotiate, that's all... There is no plan 'with Neymar' and another 'without Neymar'. The reality is that he has a contract with PSG. Today, there is no proposal."
Neymar was in Rio de Janeiro on Sunday to watch Brazil win the Copa America by beating Peru 3-1 in the final, the forward having been ruled out of the tournament by an ankle injury.