Without giving any details, and despite reports that Ferrari had joined Mercedes in refusing to supply their rivals with engines for 2016, the 84-year-old sounded upbeat at the Russian Grand Prix.
"Everything's been sorted out so I wouldn't worry about it," he told reporters.
"We don't want them to drop out. I think they have sorted it all out now," added the Briton, who said he was confident there would be 22 cars on the starting grid next year with the addition of new team Haas F1.
Red Bull's engine predicament has become the talk of the Formula One paddock, with the energy drink company owning two of the 10 teams but potentially having no power units after this season.
Red Bull Racing and Toro Rosso are currently supplied by Renault -- and had a deal for 2016 -- but that relationship has soured, with the French manufacturer seemingly set to buy troubled Lotus.
Red Bull's billionaire owner Dietrich Mateschitz has warned the teams will quit unless they have a competitive engine, which leaves only Ferrari and Mercedes -- given Honda's woeful performance with McLaren -- unless they mend fences with Renault.
Ecclestone said, however, that suggestions Mateschitz had fallen out of love with the sport were wide of the mark.
"He's never fallen out of love. He just wants to be in a position where he can be competitive. And that's what will happen. He'll be OK," he said.
Mercedes are already committed to four teams, including their own reigning world champions, and have ruled out providing dominant power units to a rival that could beat them.
Reports have indicated that Ferrari, who are already committed to three teams, would be unable to supply Red Bull with their latest specification units and reluctant also to expand to five teams.
Germany's Auto Motor und Sport reported that Ferrari were willing to supply engines to Italian-based Toro Rosso only.
A Ferrari spokesman was unable to give any details about the situation while Red Bull consultant Helmut Marko refused to comment to Reuters.
"There are a lot of negotiations going on, nothing is fixed," Red Bull principal Christian Horner told Sky Sports television.
Although Ecclestone had a long meeting with Mercedes motorsport head Toto Wolff and the team's non-executive chairman Niki Lauda on Friday, Wolff said engines had not been discussed and the manufacturer's position had not changed.
"It was a conversation about general topics," Wolff told reporters.
"Bernie doesn't twist arms, Bernie makes it very subtle," he added. "Honestly, we didn't discuss the topic (of engines)...we didn't change on our opinion."
(Editing by Amlan Chakraborty)
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