0923 GMT June 15, 2019
Most of the money would compensate 482,000 owners of two-liter diesel cars programmed to distort emissions tests, BBC reported.
Owners could receive between $1,000 and $7,000, depending on their car's age.
The agreement could still change when it is officially announced by a judge on Tuesday, sources said.
Lawyers representing car owners, Volkswagen and the US Environmental Protection Agency have not yet agreed the steps VW will take to fix the cars.
The company still faces accusations over its three-liter diesel cars, as well as the prospect of hefty fines from US regulators and possible criminal charges.
Earlier this year the German company more than doubled its provisions for the scandal to €16.2 billion.
On Wednesday VW chief executive Mueller issued a fresh apology to shareholders, saying the "misconduct goes against everything that Volkswagen stands for".
However, he has not put a figure on the total cost of the emissions scandal until a final deal was reached with US authorities.
Volkswagen admitted in September it had installed a ‘defeat device’ or software in diesel engines in the US that could detect when they were being tested.
The company subsequently revealed that more than 11 million cars worldwide were affected.
Volkswagen said it was unable to comment ahead of the court's decision.