Leonardo was on Friday named as Antero Henrique's successor in the role, which he previously held between 2011 and 2013.
Thomas Tuchel's side retained its Ligue 1 crown last season, but it exited the UEFA Champions League at the last-16 stage and the Coupe de la Ligue in the quarter-finals, before losing to Rennes in the Coupe de France final.
And following a largely underwhelming 2018-2019 campaign at the Parc des Princes, Al-Khelaifi wants PSG's players to reconsider how they conduct themselves.
"Players will have to assume their responsibilities even more than before," he said. "It must be completely different.
"They will have to do more, work more. They are not there to please themselves. And if they do not agree, the doors are open. Ciao! I do not want to have any celebrity behaviour anymore."
Al-Khelaifi acknowledged that change was required behind the scenes and is pleased with the appointment of Leonardo, who oversaw the club's takeover by Qatar Sports Investments during his first spell as sporting director.
"I realised that changes were essential, otherwise we were going nowhere," he said. "In two minutes the case was settled between [me and Leonardo].
"He will have all the sporting powers. Leo is my guy. He is incredible. I have total confidence in him. His natural authority will do good for everyone, especially the players."