As part of the settlement, Volkswagen would compensate owners of around 480,000 2.0-liter diesel cars up to USD 7,000 in cash each, and would also fund a programme to fight air pollution, the person said.
Volkswagen admitted in September that it had installed software on diesel cars that tricked US emissions tests into showing the cars met environmental standards. After testing, the device switched off, allowing the vehicles to spew up to 40 times the permitted amounts of nitrogen oxides.
The San Francisco civil lawsuit accuses Volkswagen of major damages to the environment and to the owners of the illegally rigged diesel cars.
A settlement could be enough to allow Volkswagen to avert a huge trial over how it would deal with the scandal that has already deeply damaged the world's second-largest automaker.
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To help the various sides reach a deal, the federal district court in San Francisco court recently pushed back the deadline by a week to June 28. A court hearing on the final settlement agreement is scheduled on July 26.
Volkswagen has set aside 16.2 billion euros (USD 18.4 billion) to cover the costs of the scandal, including seven billion euros for legal risks.
A settlement would not end Volkswagen's troubles in the United States.
The company needs to address similar charges over its 3.0 liter diesel cars with emissions-cheating devices. It also faces fines potentially running to the tens of billions of dollars from US regulators, and a criminal investigation over the scandal.