The company also said that Muller "showed his general willingness to contribute to the changes". This could also include a change in the position of the chairman of the Board of Management.
With Mueller agreeing to go, the controlling Porsche-Piech clan, the state of Lower Saxony and powerful labor leaders settled on Herbert Diess, chief of the Volkswagen brand, as the successor, the people said.
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.
Shares in Volkswagen surged in Tuesday afternoon trading, adding as much as five percent on the day before paring their gains to around 4.0 per cent at a price of 170.84 euros around 3:30 p.m. (1330 GMT).
The supervisory board will meet Friday to sign off on the management changes, the people said.
Diess, 59, has focused his reforms at the VW brand on procurement and process management to bring its cost structure and efficiency closer to that of rival Toyota 7203.T , but stopped short of making sweeping job cuts.
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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.
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.
While Mueller is a lifelong VW veteran, at times he cut an uneasy figure as CEO, which required him to manage the often contradictory demands of angry vehicle owners, disgruntled investors, well organized workers, and state officials with their own political agendas.
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.
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.
Volkswagen declined to comment on whether the board was poised to name Diess as new CEO.