Leonardo, PSG's sporting director, said that talks about the 27-year-old's exit were "more advanced than before," BBC Sport reported.
But the club was not ready to give its approval to a transfer, he said.
The world most expensive player has been linked with a return to Barcelona and a move to archrival Real Madrid.
Neymar joined PSG in 2017 when the club, owned by the wealthy Qatar Sports Investments, paid €222 million (£200m) to Neymar so that he could buy himself out of his contract.
The striker has scored 34 league goals in two seasons for the French giant, although injuries interrupted both of those campaigns.
PSG's coach Thomas Tuchel said Neymar took part in training on Saturday, but was not fully fit.