The former England captain moved to the Ligue 1 side in January on a five-month deal and the Qatari businessman is hoping to persuade the global superstar to stay on for another year.
"Frankly, we want to keep him with us next season," said Al-Khelaifi in an interview with L'Equipe.
"As a man, player, ambassador, he is exceptional. It creates something in this group. Everyone loves it. He is very happy in Paris.
"We will talk with him. Whatever his decision, we support David.
"Recruiting him was one of my best decisions."
Beckham has started once and made four substitute appearances for PSG since his January move and says that, despite being very happy in the French capital, he will wait to decide his future.
"We'll see. Who wouldn't want to stay at a place like this?" the 37-year-old told Le Parisien.
"It's very special but I'm not getting any younger so we'll see how I feel at the end of the season. It's always nice to be wanted."
The current owners took the reins two years ago and Al-Khelaifi is proud of what they have achieved in that time; saying that the whole country is behind them as they prepare to face Barcelona in the Champions League.
"The country is behind Paris," said Al-Khelaifi.
"For us, it is already a success to reach the last eight. This campaign has people buzzing everywhere. Us directors, players of course, staff, fans, and even the whole of French football.
"Speaking with people I feel a special excitement. It is good to feel everyone behind us.
"In France there will be always people who do not support us, but I have the sentiment that ahead of this game against Barcelona, the majority of the country pushes behind Paris."