range from less than 100 euros ($112) per vehicle to as much as 10,000 euros, depending on whether Volkswagen needs to upgrade software or install new hardware.
UBS analysts estimated the total bill for the scandal, including potential fines and lawsuits, could be around 35 billion euros, though they also noted this was more than factored into the company's share price after its recent plunge.
The supervisory board meeting, where erstwhile finance chief Hans-Dieter Poetsch is being confirmed as the company's new chairman, will receive an update from an internal investigation into the scandal, two sources close to the matter said.A representative from U.S. law firm Jones Day, which is conducting an external inquiry, will also attend.
One of the sources said it was too early to name those responsible for rigging tests, and talked of a "certain degree of fright" among management ahead of a testimony by the company's top U.S. executive before a U.S. congressional oversight panel on Thursday.
Volkswagen has come under fire in both the United States and elsewhere for a slow response to the crisis.
"We have a lot of questions. We have very few answers," complained Representative Diana DeGette of Colorado, the top Democrat for subcommittee.
Officials in Germany, where Volkswagen has been held up for years as a model of the country's engineering prowess, are also pressing for answers.
"I now expect a very transparent investigation of the circumstances. I am convinced that we will get more and more clarity," Klaus Mohrs, the mayor of Wolfsburg where Volkswagen employs around 70,000 people, told Reuters ahead of the supervisory board meeting.
Data on Wednesday showed German industrial output fell at its steepest pace in a year in August, suggesting Europe's largest economy may be losing momentum just as the Volkswagen scandal casts a cloud over manufacturing.
The car industry employs more than 750,000 people in Germany and is a major source of export income.
In his newspaper interview, Mueller rejected the suggestion Volkswagen informed financial markets too late about the test rigging despite having told officials at the U.S. Environmental Protection Agency weeks before it went public.
"Based on our understanding of the law, we informed in time," he was quoted as saying.
He also said he believed only a few employees were involved in the manipulations.
Some analysts and investors are worried that company veterans such as Mueller and Poetsch will not introduce the sweeping changes in business practices they think are necessary to restore Volkswagen's reputation.
They are also concerned about the complexity of Volkswagen's investigations.
One source close to the matter said the supervisory board of the company's flagship Audi brand would also meet this afternoon, and has hired accountants to help investigate the scandal as well.
Audi is still chaired by former Volkswagen CEO Martin Winterkorn, who resigned two weeks ago. The sources said it was unclear whether he would attend the Audi board meeting.