As the BBC explains, the diesel scrappage scheme would form part of a new plan to improve air quality.
It's thought that ministers may choose a scheme that pays drivers up to £2,000, which they can put towards buying a new, cleaner vehicle.
Yet the incentive is likely to be limited to certain drivers in order to minimise costs. Among the options are restricting the scrappage scheme to drivers who live in areas with the highest pollution; or alternatively, drivers on low incomes.
Diesel cars emit nitrogen oxides associated with conditions such as asthma, and older models tend to be the most polluting. Among the estimated 11.2 million diesel cars on the UK's roads, 17% are over 12 years old.
Figures from the European Environment Agency show that there were nearly 12,000 premature deaths in the UK in 2013 associated with nitrogen dioxide. This is Europe's second highest total, after Italy.
Chair of the House of Commons environment committee, Neil Parish, backs the scrappage plan and will use a parliamentary debate this Wednesday to address the proposal. He will likely tell MPs that government backing of £500m would take almost 10% of the 5 million 'dirtiest' diesel vehicles off the UK's roads.
In 2016, the government was urged to strengthen its plans to tackle air pollution following a judicial review that found its current proposals to be "woefully inadequate".
Under the new scrappage scheme, half of the incentive could be paid by the government, with the remaining half coming from car manufacturers. The full details of the scrappage scheme are expected to be announced in the coming days.