"The separation from our engine partner at the end of the season is by mutual agreement," Red Bull's billionaire owner Dietrich Mateschitz told Austria's Salzburger Nachrichten newspaper.
"There was no sense in working together any more. You couldn’t put the teams through that any longer."
Red Bull are now expected to switch to Ferrari after dominant Mercedes rebuffed their approaches. McLaren's partners Honda, the sport's only other engine manufacturer, are least competitive of all.
Mateschitz said Ferrari would be a "very acceptable" solution for the next two or three years.
The deal is not done, however, despite the Italian team's willingess to supply Red Bull and Toro Rosso. Red Bull consultant Helmut Marko warned that the alternative would be to walk away.
"If we don't have a competitive engine, we will leave Formula One," he told Sky Sports television at the Singapore Grand Prix.
Mateschitz was commenting after Renault head Carlos Ghosn made clear this week that the French carmaker would either buy a team or leave the sport, rather than be an engine supplier to others.
Having recorded just two podium finishes this season, both in Hungary, the team has had little to celebrate this year.
But things took a turn for the better on Friday with Daniil Kvyat setting the fastest practise time and team mate Daniel Ricciardo posting the third quickest at the floodlit Marina Bay street circuit.
It was the first time this season Red Bull had topped the time sheets in any session, a far cry from 2010-13 when they won four championships in a row and dominated the sport.
"If today's any tell-tale sign, I think we're looking pretty good," Ricciardo said. "I hoped the car would work better around here and that looks like the case."
Kvyat's performance in the second 90-minute session was all the more impressive after he missed most of the first because of engine problems.
The 21-year-old Russian, who finished second in Hungary in July, kept his cool on a steamy night to record a fastest lap time of 1:46.142 on super-soft tyres.
"Hopefully we can carry this into tomorrow, obviously everyone will be working very hard tonight but we'll try our best to stay in the same position tomorrow," he said.
(Reporting by Julian Linden, additional reporting by Alan Baldwin in London; editing by Ken Ferris)
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