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5 year oldThe Brazil forward failed to turn up for the first day of pre-season training on Monday and PSG say they will take "appropriate action".
The 27-year-old has been linked with a move back to former club Barcelona.
Leonardo added that the French champions had "not received any offers" for Neymar but there had been "very superficial contacts" with Barcelona.
Neymar joined PSG from Barcelona for a world record 222m euros (£200m) in August 2017.
Asked if the player had asked to leave the club, Leonardo - speaking to La Parisien - said: "It's clear to everyone. But in football, you say one thing today and tomorrow another. It's amazing but it's like that.
"Yes [I have spoken to Neymar]. I do not want to tell all the details of the conversation.
"We talked with his entourage too. Everyone knows everything. The position is clear for all participants.
"But one thing is concrete today: he still has three years of contract with us. And since we have not received an offer, we cannot discuss anything."
He added: "Neymar can leave PSG, if there is an offer that suits everyone.
"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 wants to rely on players who want to stay and build something big. We do not need players who would do a favour at the club by staying here."
Brazilian media quoted Neymar's father as saying that PSG "were aware" the forward was set to miss training on Monday because of charity commitments.
"The reason was known and planned for a year as part of his activities for the Neymar Institute," Neymar Sr told Fox Sports Brazil.
"We couldn't postpone them and he will return [to PSG] on 15 July."
However, Leonardo said "these were not dates agreed with the club".
"Paris St-Germain notes that Neymar Jr was not in attendance at the agreed time and place. This was without the club's prior authorisation," read a PSG statement.
"The club regrets this situation."
Neymar has scored 34 goals in 37 league appearances for PSG to help them to consecutive Ligue 1 titles, but he has also been involved in a number of disciplinary incidents, including being banned for three games for lashing out at a fan after PSG's shock French Cup final defeat.
He will also miss the next three European matches for insulting officials.
The former Santos forward was stripped of the Brazilian captaincy in May before suffering an ankle ankle injury during an international friendly against Qatar last month that forced him to miss his country's Copa America triumph on home soil.
Last week, Barcelona president Josep Bartomeu claimed Neymar wants to leave PSG this summer.
According to reports in the Spanish media, Neymar has offered to take a pay cut of 12m euros a year to facilitate a return to the Nou Camp, where he played between 2013 and 2017.
The La Liga champions side have already signed Frenkie de Jong from Ajax for an initial 75m euros (£67m) this summer and are thought to be interested in signing France forward Antoine Griezmann from Atletico Madrid.
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