The Brazilian forward has been heavily linked with a move away from the Ligue 1 champions during the close season, with his former club Barcelona looking the most likely destination.
Neymar has yet to feature for PSG so far during pre-season and was again absent as Thomas Tuchel's side laboured to a 1-1 draw with Nurnberg on Saturday.
Leonardo has previously said the 27-year-old can leave for the right price, but he told reporters after the game in Germany that no offers have been tabled for him.
"Honestly, there is nothing different from the last time we talked," he said, according to Le Parisien. "Nothing at all.
"It has not moved. There is no concrete offer for Neymar, he is with us. He is a player for Paris Saint-Germain.
"I repeat, there is no concrete offer. It's been the same situation for 10 days."
Tuchel refused to be drawn on where Neymar's future lies, two years after becoming a world-record buy, insisting he remains part of the French club's squad.
"The situation between Neymar and me is clear; it's now something between him and the club," the PSG boss said.
"He is part of the dressing room and will train with us tomorrow."