Red Star travel to Anfield for their next Champions League group game before heading home to Belgrade for the return fixture in November.
Neymar scored twice as PSG went 5-0 up before Marko Marin pulled a goal back, only for the Brazilian to complete his hat-trick with nine minutes remaining.
A Red Star official is suspected of betting 5m euro (£4.4m) on the Serbian side losing the Group C match by five goals, French newspaper L'Equipe has reported.
According to the reports, Uefa received word that a senior leader of Red Star intended, along with others, to place "several million Euros" on a defeat for the Serbian club by five goals. "FC Red Star expects to get the truth at short notice and remove any doubt about our involvement in possible wrongdoing".
With Neymar as the star of the show, PSG won the game easily.
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!"
UEFA said it did not comment on ongoing investigations.
PSG have also expressed surprise and anger over the allegations, and reaffirmed their commitment to the integrity of the sport.
"Scandalised and disgusted, Red Star Belgrade rejects suspicions concerning the PSG-Red Star game and the implication of anyone from the club in any untoward dealings", they said in a statement.
"At no time was any club member asked to discuss matters other than those strictly related to the organisation of the match, namely meetings, visits and other official lunches around every UEFA Champions League match".
"UEFA only communicates on specific cases/matches once disciplinary proceedings have been opened and/or decisions have been taken".
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