Officials in France were alerted by Uefa after a "senior leader" at the club placed the shocking bet against his own team, claim L'Equipe.
Uefa chiefs received a tip off and informed French authorities. The Sun understands French Police are investigating.
But Red Star Belgrade hit out at the claims in a statement, saying: "It is with the greatest anger and resentment that Red Star Belgrade denies the story in L'Equipe in connection to questions about the outcome of the match with PSG and the involvement of anybody from Red Star in improper actions.
"The allegations in this story could cause great to the reputation of our club.
"Therefore Red Star Belgrade insists both Uefa and the competent investigating authorities in Serbia and France investigate these claims and come to the truth.
"Today's technologies and various other mechanisms have progressed so much that it is simply not possible for this eventual case to be left unresolved.
"FC Red Star expects that the truth about this must come in as short a time as possible and that any doubt about the involvement of any member of our club in any possible disruptive actions must be removed."
The Serbian side lost the Champions League group game 6-1 and could now face action after the claims came to light.
The Belgrade club official is also reported to have had "accomplices" in the bet, with L'Equipe also claiming Uefa cottoned-on "days before" the Group C game against PSG.
Neymar scored a superb hat-trick in the riot at the Parc des Princes on October 3.
PSG had an outrageous 34 shots in the match in the French capital – to Belgrade's five.
The Ligue 1 giants also hogged the ball for the full 90 minutes, with a whopping 74 per cent possession.
On top of that, PSG had 13 corners to their opponents' zero in a match they utterly dominated.
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