The report says the 37-year-old is to return to Brazil where his wife, Giulia Reverendo Andrade, from whom he is separated, is taking legal proceedings against him over alleged abuse and death threats.
Maxwell, who has held the post at PSG since 2017 after five years as a player at the club, has denied the accusations.
"For the good of my children, I will prove my total innocence and show that this is all a lie," said Maxwell in a statement in June.
According to Le Parisien, the former left-back was no longer able to combine his activities in France with the preparations of his legal defence in Brazil.
However, PSG has proposed to the club that he represents them as an ambassador in Brazil. Sports daily L'Equipe reports that Maxwell is due to discuss the future with the club over the coming days.