Volkswagen's shares rose by more than 4 percent shortly after the first reports of the looming management reshuffle.
That plan comes as rivals including Fiat Chrysler FCHA.MI and Daimler DAIGn.DE consider spin offs or legally separate divisions to boost their share prices and raise cash to fund development of electric and self-driving cars.
Both Bloomberg and "Handelsblatt" are reporting that current VW brand chief Herbert Diess is to replace Mueller.
As CEO, Mueller led Volkswagen through the aftermath of the scandal, which included billions in fines and penalties and US criminal charges against several executives, to record sales and strong profits.
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.
The company said in its statement on Tuesday that it was considering changes to its complicated management structure.
This will hand Diess, hired from BMW in 2015, a sweeping mandate to review broader changes to the way VW's brands, which stretch from Skoda to Lamborghini, are managed.
"Diess will hold both positions, CEO of the company and the VW brand", a source familiar with the talks told Reuters on Wednesday.
Matthias Müller is likely to be replaced as chief executive of Volkswagen as the carmaker struggles to move on from the diesel emissions scandal that claimed the scalp of his predecessor.
FILE - In this June 1, 2017 file photo Matthias Mueller, CEO of the Volkswagen company, attends a contract signing ceremony as part of a meeting of German Chancellor Angela Merkel and China's Premier Li Keqiang at the chancellery in Berlin.
The debate about Volkswagen's future structure comes a month after its largest shareholder, Porsche Automobil Holding PSHG_p.DE , picked three new representatives of the Porsche and Piech families to help oversee Volkswagen. The works council, whose members occupy half the seats on the supervisory board, also declined comment.