De Ligt's performances in leading Ajax to a domestic double last term, as well as the semi-finals of the Champions League, have made him one of the world's most in-demand players.
But Juventus seem set to win the race for his signature after De Ligt's agent Mino Raiola said personal terms have been agreed with the Serie A champions.
With negotiations over the transfer fee continuing between Ajax and Juve, De Ligt was present at the start of pre-season training with the Dutch giants on Monday.
And Leonardo accepts De Ligt will not be joining PSG while indicating the Ligue 1 champions are operating to a restricted budget.
"De Ligt will not come to PSG," Leonardo said to Le Parisien. "There was a possibility.
"He is a great player but it was not a good time to make a big investment. We must calm down a little.
"We don't have an envelope with €200million to spend."
"He is a very expensive player," Leonardo added. "There is no specific project for the moment. But I do not want to talk too much about individual cases."
Leonardo said he made no offer to try and keep Adrien Rabiot at the club, with the midfielder joining Juve as a free agent.
Rabiot and Aaron Ramsey moving to Turin has led to rumors former PSG player Blaise Matuidi may now be surplus to requirements.
"I love Matuidi," said Leonardo. "I have a lot of respect and esteem for him. He has always been fundamental for PSG.
"But at PSG today, there are already players and we will continue to play 11 on the field."
PSG have signed Ander Herrera and Pablo Sarabia ahead of the new campaign, but veteran goalkeeper Gianluigi Buffon rejected a new contract to return to Juve.