Officially, the line from the company is simply that a change at the top of the company may be coming as part of a larger overhaul of management, but a number of unofficial sources (as quoted by Handelsblatt) have said Diess is likely to be appointed the new CEO soon. The surprise leadership switch is due to be finalized at a supervisory board meeting on Friday, the people said.
Mr Diess, a former BMW executive who joined VW in July 2015, has clashed with the company's labour leaders.
In 2016, a federal judge has approved a $15 billion settlement for claims following the emissions cheating controversy, making it the largest auto-scandal settlement in USA history.
Longtime CEO Winterkorn quit days after the firm admitted to installing software in 11 million diesel vehicles worldwide created to cheat regulatory emissions tests in a scandal that became known as "dieselgate". Amid opposition from labor leaders, Mueller failed to sell motorbike maker Ducati previous year.
The statement said Mueller "showed his willingness to contribute" to the changes, but stopped short of saying whether Mueller was leaving his current job. "Unions and Lower Saxony together have the power to block his appointment".
PCA officials said they received more than 1,000 public comments in recent months on how to spend Minnesota's share of the massive fines the German automaker had to pay after being caught cheating on air emissions controls on diesel cars.
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.
"Diess is ready to weather conflict, which is important to make things happen in a company like Volkswagen", said Ferdinand Dudenhoeffer, director of the University of Duisburg-Essen's Center for Automotive Research.
Board chairman Hans Dieter Poetsch said the departing Mr Mueller had done "outstanding work" at a time when the company "faced the greatest challenge in its history".
A separately listed trucks and bus business could have a market value of up to 30 billion euros ($37 billion), Evercore ISI analysts have said.
Audi and Volkswagen are the two brands to have suffered the most through the emissions difficulties, and the fact that Diess has managed to emerge with a strengthened reputation is indeed impressive.
The 59-year-old 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, but stopped short of making sweeping job cuts.
With about 642,000 employees, VW is one of the world's largest companies in every respect.