The 61-year-old subsequently clarified that he is only doing "a little consulting", and that his future "all depends" on Ecclestone, who is 86.
Ecclestone has now told Germany's Bild newspaper: "I'm staying as the boss. This will not change. I can assure everyone that everything is staying as it is."
However, it has been rumoured that Ecclestone is being marginalised by Liberty, who are keen to make changes after years with former majority owner CVC in charge.
Ecclestone explained: "It's quite simple -- the Concorde Agreement runs until 2020. Until then, the teams and the rules cannot and will not change.
"The shareholders can of course change, and the new ones will put more emphasis on advertising and commercialisation than CVC did."
"They do not control the company," he added. "They have 10 per cent of the company and for the moment, I'm still the CEO. It is the same company it has always been."
"If Liberty gets control then they can do whatever they like, as anyone can who owns a company. But at the moment they are not the owners, so they cannot do whatever they want."
And as for Brawn, Ecclestone makes clear that he is not interested in opening the door for the highly-rated engineer and manager.
"I would be happy if he went to the FIA," he said. "But he can't do anything for us at the moment. We don't need an engineer or someone with Ross' skills. I haven't spoken to him in a long time. I have no idea what he will do."
Bahrain International Circuit - Winter testing