Speculation has linked the former Ferrari technical director and Mercedes team boss to a job running the sporting and commercial aspects of F1, but Brawn told BBC Sport on Wednesday that he has not been handed such a role.
He says US company Liberty Media, which is currently undertaking a $4.4billion buyout of F1's commercial rights from present majority shareholder CVC Capital Partners, has taken him on as a consultant to help it understand how Formula 1 operates.
Autosport understands Liberty could be keen to offer Brawn a permanent role on the racing, sporting and technical side of the business in the future, once its takeover is complete, but Brawn told BBC Sport that it "all depends" on what Ecclestone decides to do in the future.
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Ecclestone remains in position as F1's CEO while the takeover proceeds, and he told Autosport Brawn's technical nous would be best suited to a role with F1's rulemaker, rather than its commercial governor.
"I'd be delighted if he went to the FIA - he would be absolutely first class," Ecclestone told Autosport.
"I haven't spoken to him for quite a long time. I haven't got the slightest idea what he could do.
"But nothing with us. We don't need an engineer, or anybody like Ross's job."
Ecclestone described speculation that Brawn has signed a deal to replace him as CEO as "a load of bollocks", but said Liberty Media could do "whatever they want to do" once they take full control of F1.
"Liberty Media are shareholders - Chase [Carey] has taken up Peter Brabeck's role as chairman, but they are not in control of the company," Ecclestone added.
"They have 10% of the company, and at the moment I am still chief executive of the company.
"It's the same company it's always been. If Liberty gains control then they are in a position to do whatever they want to do, which anybody that owns a company can do.
"But at the moment they don't own the company, so they are not in that position."
Ecclestone said he would have had prior knowledge of any move to appoint Brawn to an official position.
"Chase is absolutely no problem to deal with at all, if this had even been talked about then he would have spoken to me," Ecclestone said.
"For sure, if anyone is going to be put in that position [CEO] then I would be the person that would be doing it."
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