The Brazil international joined the Ligue 1 side from FC Barcelona for a world record 222 million euros (£198 million) in August 2017.
However, he missed large parts of the 2018/2019 campaign through injury and suspension and made just 17 league appearances, scoring 15 goals.
PSG will consider selling the 27-year-old in the forthcoming transfer window if they receive a substantial offer, a report in L’Equipe said on Sunday.
Neymar is said to be unsettled at the club and has told relatives that he was having difficulties in France.
This was even before he was accused of raping a woman in a Paris hotel in May.
The player has since denied any wrongdoing, however.
The report comes on the back of strong comments from chairman and CEO Al-Khelaifi about the attitude of squad members.
“Players will have to be more responsible than before,” he told France Football.
“It must be completely different. They will have to do more and work harder. They are not there for their own amusement.
“If they do not agree, the doors are open — Ciao! I do not want star behaviour anymore.”
His words come after a disappointing season for Thomas Tuchel’s side.
In spite of clinching the league title, they were knocked out of the UEFA Champions League at the last 16 stage by Manchester United.