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.
Red Star Belgrade have responded with the "highest anger and abomination" to a report of match-fixing by the club in their most recent Champions League match with Paris Saint-Germain.
"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.
Even though match-fixing allegations did not focus on the title race, which involved clubs such as Anderlecht, Club Brugge, and Standard Liege last season, it centred on the relegation fight and a once-famous club, FC Mechelen, which has fallen on hard times.
PSG expressed "amazement and indignation" at the allegations.
"PSG remains at the disposal of the investigators and will not tolerate the slightest attack on its reputation nor that of its officials".More news: Google introduced the new Pixel 3 mobile
"The club reaffirms its profound attachment to the fundamental principle of sport, which is and always will be the integrity of its competitions", it read.
The Champions League Group C fixture ended in a 6-1 victory for the Ligue 1 club, with Neymar scoring a hat-trick and Kylian Mbappe, Edinson Cavani and Angel Di Maria also on the scoresheet.
"The statements in this article seriously undermine our image and the club's reputation", the Serbian champions are quoted as saying.
Contacted by L'Equipe, Red Star Belgrade President Dragan Dzajic said: "You are the first to tell me about this".
"Today's technologies and various other mechanisms have progressed so much that it is simply not possible for this case to be left unresolved". I know absolutely nothing about this.
Red Star's deputy spokesman Nebojsa Todorovic informed Agence France Presse that he "cannot, in any way, comment on this", while the spokesman for Serbia's football association, Milan Vukovic, was unavailable.