"Talks are more advanced than before," Leonardo said during an informal meeting with journalists on Saturday, without providing more details about the negotiations, reports Efe news.
"We will see what happens. Everybody needs the future to be defined."
The Brazilian player was recovering from an injury and will not take part in PSG's 2019/2020 Ligue 1 opener as he has not completed a week of team training, coach Thomas Tuchel said during a press conference.
The former Barcelona player was hit twice, on Friday and Saturday, which prevented him from completing Saturday morning's training session, Tuchel said.
However, he refused to get involved in political decisions related to the forward by PSG as he said that talking about Neymar's situation is not part of his job.
Negotiations with Real Madrid would advance faster than with its rival Barcelona, the Le Parisien daily had reported earlier, citing Brazilian sources, but Leonardo did not reveal details of the talks.
It is "extremely hard to imagine" that PSG would accept a transfer for Neymar to Madrid on loan with a purchase option, the newspaper added.
The French newspaper ruled out the possibility published by the Brazilian media over the past few days.
The Spanish clubs were the only candidates to get the services of 27-year-old, Le Parisien said.
( With inputs from IANS )