"The Volkswagen group is considering further evolving the leadership structure, which could be connected with changes in the board. a change to the chief executive could be involved", VW said in a statement.
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.
Both Bloomberg and "Handelsblatt" are reporting that current VW brand chief Herbert Diess is to replace Mueller.
Muller was named CEO in 2015 after overseeing VW's Porsche brand, and has somehow led the automaker to record sales and profits as it dealt with an emissions scandal.
Predecessor Martin Winterkorn fell victim to the company's scandal over cars rigged to cheat on diesel emissions tests.
Markets reacted positively as both Porsche's and Volkswagen's shares rose by more than 4 percent shortly after the first reports of the looming management reshuffle.
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Despite facing billions in fines, vehicle refits and lawsuits relating to its "dieselgate" scandal, Volkswagen's operating results have been robust, with sales and profit hitting record highs a year ago.
"Diess will hold both positions, CEO of the company and the VW brand", a source familiar with the talks told Reuters on Wednesday.
But the persistent tug of war between its controlling families, unions and other stakeholders have made it hard to drive through structural changes that investors have said are key to the company fulfilling its potential.
The auto maker also managed to fend off Toyota Motor to retain its status as the world's largest vehicle maker.
Mueller's likely departure comes two days after Deutsche Bank DBKGn.DE , another pillar of corporate Germany, dismissed its chief executive, John Cryan, in pursuit of a more rapid turnaround following years of losses.
"We see no better alternative to Matthias Mueller to make the company fit for the future". A veteran of the company, he had previously served as head of Porsche.
A VW spokesman could not immediately be reached for comment on the expected promotion of Diess.