13 April, 2018
BMWDiess, who has been pushing for changes in the brand's structuring, joined the company in mid-2015 before the diesel scandal broke.
A VW spokesman could not immediately be reached for comment on the expected promotion of Diess.
VW said earlier on Tuesday that it was considering a change in the CEO job.
Prior to joining VW, Diess was an executive at BMW. As the executive overseeing VW's biggest unit, he has routinely butted heads with powerful labor leaders as he has sought to cut costs and simplify the carmaker's byzantine structure.
Supervisory board chief Hans Dieter Poetsch had been "speaking with different members of the supervisory and executive boards" about moving or replacing some of them, it went on, adding that Mueller "signalled he was open to play a part in the changes".
Mueller-was made CEO in September 2015, at the height of the automaker's diesel emissions scandal.More news: Fiji hand New Zealand record breaking defeat at Hong Kong Sevens
Mr Mueller, a former Porsche boss, replaced Martin Winterkorn, who stepped down as the diesel scandal rocked the automotive industry.
The company said it was contemplating a management reshuffle and reassigning responsibilities among executives that "could include a change in the position of the chairman of the board of management", the German term for CEO.
Despite the ongoing bad press and multi-billion dollar fines from the scandal, the Volkswagen Group managed to sell a record 10,521,500 passenger and light commercial vehicles previous year.
The auto maker also managed to fend off Toyota Motor to retain its status as the world's largest vehicle maker. Porsche said separately any changes at VW would have a knock-on effect for it.
However, no detail is disclosed by the company. One possibility is increased autonomy for the group's various regional and brand divisions.
The German business publication believes Mueller's ouster is being engineered by the company's major shareholders, including the Porsche and Piech families, the German state of Lower Saxony, and Qatar, who are all keen for a reboot after the Dieselgate affair.
Bloomberg's Eyk Henning contributed.