Mueller, 62, has been widely tipped to succeed Martin Winterkorn, who quit on Wednesday, when the German carmaker's supervisory board meets on Friday, and will take responsibility for the biggest business crisis in Volkswagen's 78-year history.
Shares in the world's largest carmaker by sales have plunged as much as 40 percent since Friday, when US regulators said it had admitted to fitting software on hundreds of thousands of diesel cars to detect when they were being tested, and alter the running of their engines to conceal their true emissions.
The crisis deepened on Thursday, when Germany's transport minister said Volkswagen had manipulated tests in Europe too.
"We have been informed that also in Europe, vehicles with 1.6 and 2.0 litre diesel engines are affected by the manipulations that are being talked about," Alexander Dobrindt told reporters, adding it was unclear how many vehicles in Europe were affected.
Volkswagen has said 11 million cars globally had the software fitted, but it was not activated in the bulk of them.
As well as the cost of regulatory fines and potentially refitting cars, Volkswagen faces criminal investigations and lawsuits from cheated customers and possibly shareholders.
More immediately, the new CEO will have to restore the confidence of customers and motor dealers, who have expressed frustration at a lack of information about how they will be affected by the scandal.
Mueller has a majority on the 20-member supervisory board, the source said.
Volkswagen declined to comment.
The board will also dismiss the head of the company's US operations and top engineers at its Audi and Porsche brands, a senior source told Reuters, as it seeks a fresh start.
"There will be further personnel consequences in the next days and we are calling for those consequences," Volkswagen board member Olaf Lies told the Bavarian broadcasting network.
The research and development chiefs of Audi and Porsche, Ulrich Hackenberg and Wolfgang Hatz, will be removed by the supervisory board, as will Volkswagen's top executive in the United States, Michael Horn, the senior source told Reuters.
Hackenberg and Hatz had both held senior posts at VW in development, including of engines, before they switched to Audi and Porsche. They are among Volkswagen's top engineers.
Horn acknowledged this week that the company had "totally screwed up" by deceiving US regulators about how much its diesel cars pollute.
The scandal has sent shockwaves through the car market, with manufacturers fearing a drop in demand for diesel cars and tougher regulations and customers worrying about the performance and re-sale value of their cars.
Dobrindt said Europe would agree new emissions tests in coming months that should take place on roads, rather than in laboratories, and that random checks would be made on all manufacturers.
The European Commission urged all member states to investigate the use of so-called "defeat devices" by carmakers to cheat emissions tests and said there would be "zero tolerance" of any wrongdoing.
So far, no other carmaker has been found to have used the devices.
German rival BMW said on Thursday it had not manipulated tests, after a magazine reported some of its diesel cars were found to exceed emissions standards.
Drivers worried
Friday's board meeting had originally been due to extend the contract of Winterkorn and set out a new management structure.
Though Winterkorn oversaw a doubling in sales and a near tripling in profit during his eight-year rein, he faced criticism for Volkswagen's underperformance in the United States and for a micro-management style that critics say delayed model launches and hampered its ability to adapt to local markets.