Al-Khelaifi is hopeful of reaching an agreement with Beckham within the next two weeks.
The 38-year-old former England captain announced on Thursday that he will retire from football after PSG's last game of the season. The big-spending club remains hopeful he will have a part to play in PSG's future, possibly in an ambassadorial role.
"I met him yesterday, actually, and he's very interested to continue being involved with the big project of Paris Saint-Germain," al-Khelaifi said at a news conference on Friday. "He believes in the project, he believes in the club, he loves the club."
Beckham could feature in PSG's final home game against Brest on Saturday.
"He enjoyed the last six months, so we are in discussions now. Just yesterday he announced he was going to retire, so we have time to discuss [it]," al-Khelaifi said. "In the next two weeks we are hopefully going to announce if we're going to reach an agreement together. I hope we will, because honestly I want him.
"I told him: 'The door is open for you', and he wants to be involved. So we're going to see how he's going to be involved."
The former Real Madrid and Manchester United star joined PSG in a surprise move on the last day of the transfer window and has played 13 games so far – most of them as a substitute – and clinched league title with a fourth different club, having also won two championships with the Los Angeles Galaxy.
Although Beckham has played reasonably well at times for PSG, he has actually stood out more for his combative streak than for his passing and crossing.
Beckham has set up only one goal, a delightful chipped pass from the right against Rennes that appeared to be going in anyway before top scorer Zlatan Ibrahimović helped himself to another goal.
Beckham was booked in the second leg of the Champions League quarterfinal against Barcelona, and against Evian on April 28 he was red-carded shortly after coming on as he went into a tackle with a dangerously raised foot. There was no contact, but the challenge was reckless.
Against Brest at Parc des Princes on Saturday, Beckham will have a chance to say farewell to PSG's fans, who only knew him for a short time, before pulling on a jersey for the final time in Lorient. – Sapa-AP