The pair have been in talks to extend their stay at the Parc des Princes, with PSG sporting director Leonardo confirming last week he is hopeful of "good news" regarding their contract renewals.
Speaking to SkySports in Italy on Wednesday night after Paris Saint-Germain qualified to the Champions League semi-finals on away goals against German club Bayern Munich, Al-Khelaifi seemed more confident with his two star players to long-term stays.
"I think that next year Neymar will be at Paris Saint-Germain and he will stay here for a long time," Al-Khelaifi said. "Him and Mbappe have no reason to leave.
"It's been a fantastic night for us. We could have scored three or four goals, it's something wonderful. I'm proud of my players.
"Now we'll aim to win the Champions League. It's the second year in a row we're in the semi-finals, it's a great success."