Volkswagen is reported to have reached a deal with the US authorities in its bid to settle its diesel emissions cheating case. Part of the settlement involves paying its US customers $5,000 each.

The cash settlement alone will cost more than $1bn. This does not include the cost of buying back vehicles should the owners choose to sell them back to VW.

Germany's Die Welt reported on 20 April that the settlement is expected to be presented to Judge Charles Breyer in San Francisco on 21 April. If he accepts it, VW will avoid going to trial that has been fixed to be heard in the summer.

A US federal judge had given both VW and regulators until 21 April to reach an agreement on how to resolve the issue of nearly 600,000 diesel cars in the US that have been affected by the car-maker's emissions test-rigging scandal.

Two people briefed on the matter, told Reuters that as part of the settlement, VW has agreed to buy up to 500,000 2.0 litre diesel vehicles sold in the US. This includes the Jetta sedan, the Golf compact and the Audi A3.

The buyback offer does not extend to the bigger 3.0 litre diesel vehicles which had also exceeded US pollution limits. This includes the Audi and Porsche SUV models, the sources said.

It is believed that the carmaker is thought to have also offered to repair the vehicles if the US regulators approve the repairs as workable. It is believed that cash compensation will be given to owners who either sell their vehicles back to VW or opt to have them fixed.

Those who sell back their vehicles, will get an additional cash payment on top of receiving the estimated value of the vehicles, fixed at the time before the scandal became public in September 2015.

VW car owners have around two years to decide on which option they wish to take up. The source told Reuters that it is not clear whether VW will be able to resell the vehicles that they are forced to buy back.

VW, the US Environmental Protection Agency and the Justice Department declined to comment, Reuters said. In December last year, VW announced the setting up of an independent claims programme for affected car owners. It named Ken Feinberg, a compensation expert who had handled funds for the 9/11 attacks, BP Deepwater Horizon oil spill and the General Motors ignition switch crashes, to administer its programme.

The carmaker has already rejected similar compensation claims from Europe, saying that there were no grounds to replicate the compensation programme it was offering in the US. It had earlier agreed to pay a goodwill compensation worth $1,000 each to owners of vehicles found to be in breach of the US emissions limits.

VW admitted in September last year that it had cheated US environmental tests by using software to mask nitrogen oxide emissions that can cause or exacerbate respiratory disease.