A government scheme expected to be announced this week would offer drivers up to £2,000 to trade in their old diesel car for a greener alternative.
It would mirror the so-called "cash for clunkers" in 2009, which took 400,000 of the most polluting diesels off UK roads, the BBC says.
As then, the government will offer £1,000, matched by £1,000 from vehicle manufacturers, as a discount on a new lower-emission car when trading in an old diesel.
The Week
Escape your echo chamber. Get the facts behind the news, plus analysis from multiple perspectives.
SUBSCRIBE & SAVE
Sign up for The Week's Free Newsletters
Join more than 350,000 subscribers and keep yourself informed with a selection of The Week’s most interesting, enlightening and entertaining stories - plus daily puzzles.
Join more than 350,000 subscribers and keep yourself informed with a selection of The Week’s most interesting, enlightening and entertaining stories - plus daily puzzles.
Latest Videos FromThe Week
But The Times says the project is unlikely to be universal and instead be targeted to those in certain areas or on lower incomes.
"Ministers have decided that a universal scheme would be too expensive and likely to benefit only pensioners in rural areas who rarely drive their diesel cars, thereby making it unlikely to reduce pollution significantly," the paper says.
It adds: "There are more than 11 million diesel cars on British roads and about two million of them are more than 12 years old.
"Restricting a scrappage scheme to the oldest cars in the worst-polluted cities - London, Birmingham, Nottingham, Leeds and Derby - could lead to as many as 150,000 vehicles being scrapped, according to one analysis."
Neil Parish, chairman of the Commons environment committee, is expected to tell parliament on Wednesday that government funding of £500m would take nearly half a million of the dirtiest cars off the road.
Diesel cars have boomed since the late 1990s thanks to incentives such as cheaper road tax from the then Labour government, offered because diesel emits less carbon dioxide and so contributes less to climate change.
However, in recent years it has emerged that diesel cars produce very high levels of particulate nitrous oxide emissions which are linked to respiratory disease and are the reason many UK cities breach EU clean air laws.
One option to solve the problem would be to tax diesel cars more, but Prime Minister Theresa May has said she does not think it acceptable to punish drivers who were encouraged by Labour to buy diesel cars.
