The prosecutor said they would provide more information on the arrests of Galtier and his son John Valovic-Galtier - a player's agent - via a statement later on Friday.
Galtier is set to be fired by the Qatari owners of PSG after a largely underwhelming season in which PSG suffered 10 defeats in 2023, exiting the Champions League, the team's main objective, in the last 16.
The allegations first surfaced in the French media in April.
The reports - which AFP was unable to verify - alleged that ex-Nice sporting director Julien Fournier had written an email at the end of the 2021/22 season in which he claimed Galtier had made discriminatory remarks at several members of the Nice squad.
"He (Galtier) told me that I should take account of the reality of the city and that in effect we should not have as many Blacks and Muslims in the team," claimed Fournier, whose relationship with Galtier was a fraught one.
"He told me he wanted to profoundly change the team's make-up and limit the maximum number of Muslims."
Galtier said he was "deeply shocked by the claims" and denied the allegations. He launched a defamation suit of his own against the journalist who published the claims and Fournier.
Fournier indicated to AFP on May 22 he had been questioned as part of the judicial enquiry without giving any further details.
Several players and directors, including the club president Jean-Pierre Rivere, and former coach Didier Digard were also questioned by investigators.
The message was reportedly sent by Fournier -- whose relationship with Galtier was tense -- to Dave Brailsford, the former head of British Cycling and Team Sky now the Director of Sport at Ineos, the owners of Nice.
Galtier and Fournier both left Nice last year after working together at the club for one season, with the former being appointed by PSG.