"We didn't reach an agreement - he's a great player, I met him and it's bad luck we didn't reach an agreement," Al-Khelaifi said on the sidelines of a news conference in Doha.
"We weren't far [from reaching an agreement], but there are family issues and I think that was the reason. It was very difficult to move the family."
The former England captain had been linked with a possible move to the Qatar-backed Ligue 1 pacesetters last month given that his contract with Los Angeles Galaxy ran out on December 31.
However with four children and his singer and fashion designer wife Victoria based in California, the move fell through.
"It's over. It's a shame. But the welfare of his family in Los Angeles, the wish not to change everything in his life, weighed heavily," said PSG Sporting Director Leonardo.
Al-Khelaifi told French radio station RMC the 36-year-old midfielder would stay in the United States, saying: "David Beckham is in Los Angeles and he's going to stay over there."
The Parisian club's new Qatari owners bankrolled a close-season spending spree of some 85 million euros, almost half of which went on snapping up Argentina international Javier Pastore from Palermo.
Their ambition was highlighted last week when they appointed Italian Carlo Ancelotti as their coach, having parted ways with Antoine Kombouare despite the club being top of the French league at the mid-season break.
