Two sources have told the Associated Press that the Volkswagen Group has reached a tentative agreement with various government agencies, and that full details of the settlement will be announced on Tuesday (US time) by San Francisco district court judge Charles Breyer.
According to the sources - who asked to remain anonymous due to a gag order on the case - the bulk of the money will go towards compensating owners, and fixing or buying back affected vehicles.
The remainder of the cash will be used to pay government penalties and remediate the environmental damage caused the cars' extra pollution.
The roughly 482,000 US owners of Volkswagen and Audi cars fitted with the EA189 2.0-litre turbo-diesel engine will be given the option of selling their cars back to the company, or have all dieselgate-related fixes applied for free.
It's understood that Volkswagen and the Environmental Protection Agency (EPA) have yet to agree on a fix for affected vehicles, although it will likely involve the installation of a larger catalytic converter and a urea injection system.
Regardless of whether owners decide to keep their cars or sell them back, all are in line to receive between US$1000 and US$7000 ($1350 and $9500) in cash. Compensation will average around US$5000 ($6750), with the exact amount determined by the car's age.
This settlement only cover cars sold in the USA with the EA189 2.0-litre turbo-diesel engine. The emissions testing defeat device fitted to the 3.0-litre V6 TDI engine used in various Volkswagen, Audi and Porsche models is subject to separate legal action.
One source warned that the agreement's details could change between now and its official announcement next week.
If the US$10.2 billion figure proves to be accurate, it will dwarf previous automotive settlements, including General Motors' recall of faulty ignition switches, which is estimated to have cost the automaker around US$6.9 billion ($9.3 billion), including a US$900 million ($1.2 billion) fine.
In September 2015, when Volkswagen publicly admitted to using software to cheat its way past laboratory emissions tests for 11 million cars sold worldwide, it set aside 16.2 billion euros ($24.7 billion) to pay for the associated remediation costs, buy backs, litigation and fines.