Sakho spent six seasons with the Parisian giants before moving to Anfield in 2013 and has made 80 appearances for the Merseyside club in all competitions.
However none of those have come this season, with boss Jurgen Klopp freezing the 26-year-old out of his first-team plans after questioning his attitude.
Reports suggest that Turkish giants Galatasaray are keen to bid for the defender and he may well be allowed to leave during the current transfer window.
A move back to the French capital has been suggested but, while it may well suit all parties, there has been no dialogue.
"I love Mamadou Sakho as a player and as a person, too," Al-Khelaifi told Infosport+. "But we have not spoken to him.
"We will talk with the coach and players and see if there is need to change things. We have until January 31 to decide whether to sell or lend some players but there is nothing officially recorded."
Ligue 1 last week