The German auto maker would offer to repair or buy back the affected diesel vehicles and pay owners compensation, according to sources close to the talks.
In 2015, US regulators discovered that VW cars were fitted with software that could distort emissions tests.
VW subsequently said 11 million cars were affected worldwide.
The US settlement is still pending approval by a judge, but it would be the largest car scandal settlement in the country’s history. The details are expected to be announced on June 28.
According to news agencies, the legal settlement sets aside $10 billion to repair or buy back around 475,000 affected vehicles with 2-litre diesel engines, and to compensate owners with a payment of up to $10,000.
Car owners would still be able to decline the VW offer and sue the company on their own.
According to the sources quoted by news agencies, the deal also includes $2.7 billion in funds to offset excess diesel emissions and $2 billion for research into green energy and environment-friendly cars.
VW installed software in diesel engines to detect when they were being tested so the cars could cheat the results.
Some models could have been pumping out up to 40 times the legal limit of the pollutant, nitrogen oxide, regulators disclosed.
The company told its shareholders last year it had set aside $7.3 billion to help defray the potential costs of a recall or regulatory penalties.
That amount though might not be enough – VW faces as much as $20 billion in fines for Clean Air Act violations alone.
The increased emissions provision pushed VW to an annual pre-tax loss of €1.3 billion, compared with a profit of €14.7 billion the previous year.
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