The retired midfielder has revealed he and several teammates were approached to throw the European cup final against Marseille in return for money 22 years ago.
The Serbian club went on to triumph 5-3 on penalties in Bari 22 years ago, but, according to Savicevic, several players had been approached by unnamed figures in their hotel rooms on the eve of the clash.
"It's not a secret," Savicevic said in an interview with the Associated Press. "I have been saying this for a while and I have never denied it: 500,000 marks was offered to us.
"We refused it because it is not in our character. Everyone knows it ... ask [goalkeeper Stevan] Stojanovic, or [midfielder] Robert Prosinecki."
The former midfielder, who is now head of Montenegro's football association, went on to lift the Champions League trophy for a second time with AC Milan in 1994.
Marseille, meanwhile, won the Champions League in its inaugural season in 1992-93, but had its Ligue 1 title stripped amid a match-fixing scandal.