Leonardo told reporters Saturday that exit talks regarding the 27-year-old are "more advanced than before." He also denied there was an agreement between the French giants and interested parties.
"We will see what happens - everybody needs the future to be defined," he added.
PSG manager Thomas Tuchel also spoke with the press ahead of Les Parisiens' Sunday clash with Nimes and offered an explanation for Neymar's absence.
"He is in an individual training phase, in and out of collective sessions," the German said. "He is still a little injured. He took a knock today (and) did not do a full week."
Barcelona president Josep Maria Bartomeu stoked the fire earlier in the summer when he alleged his club was aware Neymar wanted to leave the French capital. Antonie Griezmann's big-money move to the Camp Nou has prompted rumors that Barcelona fancy a swap deal for Neymar in hopes of skirting Financial Fair Play rules; Philippe Coutinho's name is most commonly cited as a potential makeweight.