Mercedes have enjoyed a more harmonious atmosphere within the garage since the departure of Nico Rosberg as champion at the end of 2016, but Ecclestone wants the drama to return with a Hamilton-Vettel super team in 2021.
"I'd like to see him [Vettel] in Mercedes," Ecclestone told RTL. "Obviously, I'd like to see him against Lewis Hamilton.
"I think that would be good for Formula 1, good for the sport, good for the people that are watching Formula 1."
The rivalry between Hamilton and Vettel reached a head at the 2017 Azerbaijan Grand Prix, when Vettel, believing that Hamilton had brake-tested him, pulled alongside the Mercedes and turned into him.
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Since then, the two drivers have developed a healthy respect for one and other.
Ecclestone added: "I think both of them get on with each other without any problems. It's not a case of being what their egos are, both of them have got super talent. So, it would make a super, super team.
"I don't see any problem with Lewis being concerned at all, and I know that Sebastian would love to have the opportunity to race against him."
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