The Brazilian and French forwards have been linked with moves this summer after another disappointing Champions League campaign for the Ligue 1 champions.
And president Nasser Al-Khelaifi is fed up with the mentality of his squad and wants to see improvements with those unwilling to cooperate set to be shown the door.
“The players are going to have to assume their responsibilities even more than before,” Al-Khelaifi said.
“It has to be completely different. They will have to do more, work more. They are not here to have fun.
“And if they don’t agree with this point of view, the doors are open. Ciao!
“I no longer want to have superstar behaviour.”
The front page of L’Equipe on Monday reads: “Le Chant du Départ” (Departure Song), signalling the potential for the £200m signing to leave after two underwhelming seasons.
Injuries have prevented Neymar from inspiring PSG in Europe, with both exits in his two seasons with the club coinciding with his absence.