Volkswagen is close to completing a deal to resolve claims in the United States over its admission that it rigged vehicles to cheat on pollution tests, according to three people involved in the case.

A deal, if completed, is expected to include fines from regulators and compensation to owners that could collectively cost Volkswagen billions of dollars. The three people spoke on the condition of anonymity, citing the continuing legal matter.

Even at a high price, a settlement would be a major relief to the car company. The uncertainty over the financial impact of the deception has delayed its earnings reports and impaired its ability to raise money on the markets.

Judge Charles Breyer of the United States District Court in San Francisco had given Volkswagen until Thursday to reach a settlement with the federal government and with vehicle owners in the United States. The judge has scheduled a hearing in the case for Thursday morning.