The CEO was due to have his contract extended at a supervisory board meeting on Friday, but is now facing questions over why the scandal wasn't averted.
The Tagesspiegel newspaper, citing unidentified sources on Volkswagen's supervisory board, said the board would decide on Friday to replace the 68-year-old with Matthias Mueller, the head of the automaker's Porsche sports car business.
A Volkswagen spokesman denied the report. Winterkorn did not mention his future in a video message posted on the company's website in which he repeated his apology for the scandal.
A key Winterkorn ally withheld public support for the under-fire chief executive.
"I don't want to preempt the upcoming intense deliberations and will not comment on details or any consequences," Stephan Weil, head of the German state of Lower Saxony, told reporters in Hanover when asked about Winterkorn's future.
Weil, a supervisory board member representing Volkswagen's second-largest shareholder, earlier this year helped Winterkorn to see off a challenge to his leadership by long-time chairman Ferdinand Piech and earlier this month backed the CEO's contract extension.
Shares in Europe's biggest carmaker plunged almost 20 percent on Monday after it admitted using software that deceived U.S. regulators measuring toxic emissions in some of its diesel cars.
The stock tumbled another 20 per cent to a four-year low on Tuesday after some countries in Europe and Asia said they would launch investigations themselves. Preference shares were down 19.7 percent at 106.1 euros at 1500 GMT.
At the lowest point, the falls in the preference and ordinary shares wiped more than $30 billion off the company's market value.
Volkswagen said it would set aside 6.5 billion euros ($7.3 billion) in its third-quarter accounts to help cover the costs of the biggest scandal in its 78-year-history, blowing a hole in analysts' profit forecasts.
It also warned that sum could rise, adding diesel cars with so-called Type EA 189 engines built into about 11 million Volkswagen models worldwide had shown a "noticeable deviation" in emission levels between testing and road use.
Volkswagen sold 10.1 million cars in the whole of 2014.
The U.S. Environmental Protection Agency (EPA) said on Friday Volkswagen could face penalties of up to $18 billion for cheating emissions tests.
The carmaker also faces lawsuits and damage to its reputation that could hit sales, and media reports have said the U.S. Department of Justice has opened a criminal inquiry into the matter.
The crisis has sent shockwaves through Germany, with Chancellor Angela Merkel calling for "complete transparency" from a company long seen as a beacon of the country's engineering excellence, and newspapers putting the blame squarely on Winterkorn.
The CEO was due to have his contract extended at a supervisory board meeting on Friday, but is now facing questions over why the scandal wasn't averted.
Volkswagen, which for several years has been airing U.S. TV commercials lauding its "clean diesel" cars, was challenged by authorities as far back as 2014 over tests showing emissions exceeded California state and U.S. federal limits.
The company attributed the excess emissions to "various technical issues" and "unexpected" real-world conditions.
It wasn't until the EPA and the California Air Resources Board threatened to withhold certification for its 2016 diesel models that Volkswagen in early September admitted its wrongdoing.
"Winterkorn either knew of proceedings in the U.S. or it was not reported to him," Evercore ISI analyst Arndt Ellinghorst said. "In the first instance, he must step down immediately. In the second, one needs to ask why such a far-reaching violation was not reported to the top and then things will get tough too."
Porsche's Mueller was promoted to Volkswagen's executive board on March 1 and was previously its head product strategist. As a management board member of family-owned Porsche SE, he is also close to the Porsche-Piech clan that has a controlling shareholding in Volkswagen.
"TOTALLY SCREWED UP"
Winterkorn has built Volkswagen into a global powerhouse since he took the helm in 2007, with brands ranging from budget Seats and Skodas to premium Audis and top-end Lamborghinis.
But he has also faced criticism for a centralised management style which some analysts say has hampered the company's efforts to address long-standing underperformance in North America.
Workers in Wolfsburg, where Volkswagen employs over 50,000 people, were dismayed by the damage to the company's image. "If Winterkorn knew of the manipulation, then he must go," said one staffer who works at the plant's human resources department.
Late on Monday, Volkswagen's U.S. chief Michael Horn said the company had "totally screwed up" and promised to make amends.
There have been no suggestions so far that other carmakers have engaged in the same practices as Volkswagen. Germany's BMW and Daimler have said the accusations against Volkswagen did not apply to them.
But shares in rivals including Peugeot, Renault and Fiat Chrysler fell on Tuesday amid signs regulators across the world will step up scrutiny of vehicle tests, which environmentalists have long criticised for exaggerating fuel-saving and emissions results.
"No doubt we will hear a lot from plaintiffs’ attorneys representing the poor car buyers but I guess the group that would have been hurt most would have been the other car manufacturers who compete with Volkswagen," said one Swiss-based hedge fund manager, speaking on condition of anonymity.
The EPA said on Monday it would widen its investigation to other automakers, and French Finance Minister Michel Sapin said on Tuesday an EU-wide inquiry was needed too.
Germany's transport ministry said it would send an investigative commission to study whether cars built at Volkswagen's headquarters complied with German and European emissions guidelines. Switzerland and Italy also said they would investigate Volkswagen's diesel vehicle emissions tests.
The European Commission said it was in contact with Volkswagen and U.S. authorities, and it was premature to say whether specific checks on the carmaker's vehicles were needed.
In Asia, South Korea's environment ministry said it would investigate 4,000 to 5,000 of Volkswagen's Jetta, Golf and Audi A3 vehicles produced in 2014 and 2015, and could expand its probe to all German diesel cars if it found problems.
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