Mercedes - who have Britain's 2008 world champion Lewis Hamilton and Germany's Nico Rosberg as their F1 drivers - said they did not comment on speculation. Williams also had no comment.
If the unsourced report is confirmed, the move would be seen as a major setback for former champions Williams as they prepare for the new season starting in Australia on March 17.
The Austrian was handed a far more hands-on role in July last year, working closely with team founder and principal Frank Williams. He has also guided the career of the team's new Finnish driver Valtteri Bottas.
Wolff's compatriot Niki Lauda, the retired three-times world champion, was appointed non-executive chairman of the board of the Mercedes Formula One team after Haug's departure was announced last month.
Bild said on their website (www.bild.de) that the move could be announced at a DTM (German Touring Car) test at the Valencia track in eastern Spain starting on Tuesday.
Wolff, whose Scottish wife Susie drove a Mercedes in the DTM, is a shareholder in HWA AG which runs a Mercedes DTM team and works with Mercedes in Formula Three. (Reporting by Alan Baldwin, editing by Pritha Sarkar)
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