Volkswagen has agreed to pay up to $14.7 billion to settle claims stemming from its diesel emissions cheating scandal, in what would be one of the largest consumer class-action settlements ever in the United States.

The proposed settlement involving the federal government and lawyers for the owners of about 475,000 Volkswagen vehicles, includes a maximum of $10.03 billion to buy back affected cars at their pre-scandal values, and additional cash compensation for the owners, according to two people briefed on the settlement’s terms.

The cash compensation offered to each car owner will range from $5,100 to $10,000. Both the buyback price and amount of the additional compensation will depend on the cars’ value before Volkswagen’s public admission last September that its supposed “clean diesel” cars had been deliberately designed to cheat on air-quality tests.

Despite the scope of the deal, which would still require the approval of the federal judge overseeing the case, the settlement would cover only a small fraction of the 11 million diesel cars worldwide — most of them in Europe — that Volkswagen has acknowledged contained the cheating software.