It is claimed that, in the days leading up to the match, UEFA was informed that a senior figure at the Serbian club was planning on placing almost €5 million (£4.4 million) on his own team to lose by five goals.
Red Star Belgrade issued a statement rejecting the allegation "with the highest anger and abomination".
It alleged that some Red Star players were talked into getting involved on the eve of the game, and said the official had a meeting with PSG chairman and CEO Nasser Al-Khelaifi scheduled that did not eventually take place.
Both clubs have denied any wrongdoing.
PSG "categorically rejected" the claims in a statement and said that the club "will not tolerate the slightest attack on its reputation".
According to L'Equipe, the prosecutor's office was alerted by Uefa days before the 3 October game at the Parc des Princes.
"Allegations from L'Equipe could cause considerable damage to our club's reputation and Red Star Football Club therefore insists that UEFA as well as the authorities in Serbia and France should fully investigate these suspicions to find out the truth", Red Star said.
"The club reaffirms its profound attachment to the fundamental principle of sport, which is and always will be the integrity of its competitions".
The Serbian club released a statement as well and denied the reports.
Contacted for comment by L'Equipe, honorary Red Star president Dragan Dzajic said: "This is the first that I have heard of it", and that he knows "absolutely nothing about this - it is not possible, it is untrue!"
"Today's technologies and various other mechanisms have progressed so much that it is simply not possible for this case to be left unresolved".
Neymar scored a hat-trick in the riot to add on to goals from Edinson Cavani, Angel Di Maria and Kylian Mbappe.
PSG host Napoli next, while Red Star visit Liverpool.
ARJEL, the body tasked with regulating online gambling in France, told the newspaper it had not noticed any suspicious betting patterns on the game.