There were rumours that Neymar was in Doha to complete a medical on Monday but those proved to be unfounded as the 25-year-old put up a post on Instagram suggesting that he was flying back to Spain from a commercial trip in China.
Al-Khelaifi refused to comment on the future of a player not contracted to PSG but hinted at developments to come when he admitted that he hopes "to talk about it another time".
"I think this question is a bit hasty," he replied when asked by Medi1 TV if the transfer was set to be completed. "Today, Neymar is a Barcelona player and we'll see what will happen with him.
"But we respect all contracts signed between other clubs and players. I don't really want to talk about it at this time. I hope to talk about it at another time.
"I prefer not to give percentages, either, but everything in its own time..."
Al-Khelaifi did confirm, however, that PSG are in the market for star talent who can help to bring both silverware and substantial publicity to the Parc des Princes.
"Neymar is a world star, but I repeat, he's a Barcelona player today," he said.
"Bringing in a star is not only a question of name or reputation, but also the style of play. PSG have the ambition to have great players who are recognised around the world, to increase the reputation of the club and give the players and the coach the level to which we aspire."