The report suggests Brawn will be replaced by former McLaren technical director Paddy Lowe, who joined Mercedes as an executive director earlier this year.
UPDATE: Monday, Oct. 7, at 11:55 a.m. BST
Mercedes has moved to play down talk of Brawn's exit, tweeting:
---End of update---
Brawn previously won seven world titles alongside Michael Schumacher with Benetton and Ferrari, where he worked as technical director and devised race strategies.
In 2009 he followed that success as team principal of his own Brawn team, where British driver Jenson Button led the debutant outfit to world championship success.
The Bild report, via TheStar.com, suggests Brawn is now set to work with McLaren and Japanese engine manufacturer Honda, which will supply engines from the 2015 season, when the British company's ties with Mercedes will end.
Any move would reunite Brawn with former driver Button at the Woking-based outfit from next season, with the team hoping to recover from what has been a disappointing 2013 season thus far.
With technical requirements set to undergo another big change ahead of 2014, as discussed by McLaren sporting director Sam Michael, per Formula1.com, the capture of Brawn would be a major boost for the British outfit.
Team principal Martin Whitmarsh is keen to recruit a top partner for Button, with Fernando Alonso recently mentioned according to the Telegraph's Tom Cary. Added to Brawn's reported arrival, McLaren looks set to make big moves this winter as it seeks to advance from this season's lowly fifth place.
Per Autoweek.com, McLaren announced losses of $5 million for the 2012 season last week, but that will not deter the team from making bold moves as it attempts to return to the top of the sport.
For Mercedes, Brawn's exit would be the latest move in a reshuffle of the team's management, after what has been a disappointing season.
Having showed signs of promise at various stages of the campaign, it has been unable to challenge the supremacy of Red Bull and is now competing with Ferrari for second place in the title race.
Executive director Toto Wolff recently told NBC Sports that the team was "disappointed" with recent results and the hope will be that, despite the loss of Brawn's experience, a change of leadership will bring success to the German manufacturer.