The 59-year-old Diess looks set to retain his responsibilities as head of the core VW passenger auto brand if he becomes the group's next CEO, the second source said.
German carmaker Volkswagen told press on Tuesday that the automotive giant is considering far-reaching personnel changes within its senior management. The 64-year-old Mueller has two years left on his current contract.
In the aftermath of the diesel-cheating scandal, Volkswagen has been pushing to overhaul its rigid top-down management structure, delegating more responsibility to its brand and regional chiefs.
Last month, Mueller said that chief executives of big companies deserved high pay because "one always has one foot in jail".
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He, Laschet and Reul laid flowers in central Muenster and paid their respects to the victims of the attack. German Chancellor Angela Merkel said she was "deeply shocked by the bad events in Muenster".
He launched an ambitious reform plan, including investing billions of euros in electric vehicles, but has struggled to push through reforms aimed at creating a more efficient and focused company. Amid opposition from labour leaders, Mueller failed to sell motorbike maker Ducati past year. Diess joined VW from German rival BMW in mid-2015, shortly before the scandal erupted publicly.
Previous executives who attempted deeper cuts in VW's homeland, including Bernd Pischetsrieder and Wolfgang Bernhard, were forced out of office or stifled in their reform efforts. Other potential CEO candidates include Volkswagen's trucks chief and Daimler veteran Andreas Renschler.
Shares in Volkswagen, which also owns the Bentley, Bugatti, Lamborghini, Skoda, Audi and Porsche brands, jumped on the news, and were up 4.3 percent at 171.24 euros at 1520 GMT.
Diess is due to outline the group's new leadership structure in front of the supervisory board on Friday, two sources said. No further information was made available with regards to the precise fate of acting CEO Matthias Mueller.
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The two leaders also discussed the special category status promised to Andhra Pradesh. We condemn this and completely support their demand", the chief minister said.
As CEO, Mueller led Volkswagen through the aftermath of the scandal, which included billions in fines and penalties and USA criminal charges against several executives, to record sales and strong profits.
Citing company sources, the German newspaper Handelsblatt reported that Mueller is about to be replaced by Herbert Diess, an executive who now leads the Volkswagen brand.
The automaker said in a statement Tuesday that it was in discussions with top executives and members of its supervisory board that may result in changes to personnel.
Its complex structure has extended to its main shareholder, Porsche Automobil Holding, where VW's chairman serves as the CEO and Mueller also serves as a top executive.
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