Speculation has been bubbling away all season about Brawn's future, with a decision due to be made after the campaign about whether he will remain or hand over responsibility to Paddy Lowe.
The BBC reported this week that Brawn's mind was made up and that he was definitely leaving next year, perhaps for another job in Formula 1.
But Lauda, who has long been an ally of Brawn's, still believes he can convince Brawn to remain on board, and says matters will not be sorted until after the final race in Brazil.
"The speculation is total rubbish," Lauda was quoted as saying by The Times. "The situation is absolutely clear.
"I spoke to Ross a while ago and we agreed that he will come back to me after the final race of the season in Brazil to tell me whether he wants to stay or go.
"I am trying everything I can to encourage and motivate him to stay. I am the one who asked him to stay.
"I want him to do it but it is not my decision, it is his decision. If he stays he will be team principal - nothing else - or he will retire."
Brawn has said several times in recent weeks that he will only stay on board if he feels his power to run the team the way he wants to remains intact.
Mercedes itself has declined to comment on the reports that Brawn is definitely leaving, with it non-committal about whether or not the Briton will stay in 2014.
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