The UK Government is expected to announce within days a limited diesel scrappage scheme for cars.
However, it met with a lukewarm response from the motoring industry, and is opposed by public transport campaigners.
Help with retrofitting engines to make them cleaner would also be offered to van owners.
The move is understood to be part of ministers’ new air quality strategy, which they had tried to postpone until after the general election.
However, the High Court ordered its publication by next Tuesday following a legal challenge by environmental groups.
The scrappage scheme would be limited to vehicles over a certain age and registered in areas where air pollution is already at dangerous levels,
There are 23 pollution zones - or "air quality management areas" - in Scotland where particulates, the most harmful of diesel emissions, are a particular problem.
They lie across the Central Belt and in Fife, Perth & Kinross, Dundee and Aberdeen.
Nitrogen dioxide, another diesel pollutant, is also a problem in East Lothian and the Highlands.
The expected scrappage scheme follows Prime Minister Theresa May indicating that drivers of older diesel cars would not be penalised if the Government cracks down on such engines to protect health.
Motorists were encouraged to switch from petrol to diesel under Tony Blair’s Labour government and Mrs May has said that would be taken “into account” in future plans.
Past policy was to cut carbon emissions to reduce global warming by encouraging more efficient diesel engines, but they produce more emissions that are harmful for health than petrol engines.
A scrappage scheme in 2009 involved owners of cars at least ten years old being offered Â£2,000 to trade them in for new models.
Phil Gomm, of the RAC Foundation, said: “We see a strong case for retrofitting the biggest, oldest, most polluting buses, lorries and taxis that do the most mileage around our towns and cities.
“We are less convinced about a car scrappage scheme, even one targeting the oldest models.
“It is one thing identifying where a supposedly ‘dirty diesel’ is registered, but there will be little to no information on where, when and how far it is driven, which are the crucial factors.
“It is quite possible the most serious polluters are cars only a few years old.”
Tamzen Isacsson, spokeswoman for the Society of Motor Manufacturers and Traders, which represents the industry in the UK, said: "While we support fleet renewal in principle, any scheme would have to deliver value for money for the public and must therefore be developed carefully.
"Environmental benefits must be maximised without destabilising the market or confusing consumers.
"Air quality is largely a local issue, which means any scheme would need to be carefully managed to ensure it is effective.”
Public transport campaigners and some transport experts said cleaning up bus engines would have a far greater impact.
David Begg, publisher of Transport Times magazine and a former Edinburgh City Council transport convener, said: “In terms of value for taxpayers’ money, retrofitting buses offers 15 times more than a diesel car scrappage scheme.
“A scrappage scheme for buses offers 11 times more value than the diesel car option, yet all the talk in the media relates to diesel car scrappage.”
Colin Howden, director of sustainable transport campaigners Transform Scotland, said: "Rather than subsidising private car users, the UK Government's first priority should be to invest in less polluting public transport services.
"A scrappage scheme for buses, or retrofitting existing ones, would be a more cost-effective way of bringing about a cleaner vehicle fleet.
"The UK Government should provide the Scottish Government with the option of prioritising investment in public transport services rather than subsidising drivers."
A spokeswoman for the Scottish Government’s Transport Scotland agency said: “We have no current plans to introduce a vehicle scrappage scheme in Scotland.
“However, as part of our Cleaner Air for Scotland strategy, we will work with the UK Government to investigate the merits of a scrappage scheme for the oldest, dirtiest vehicles.”
Emilia Hanna, air pollution campaigner at Friends of the Earth Scotland, said: “Some kind of scrappage scheme to enable the transition to cleaner modes of transport is welcome, but it would need to be done carefully.
“We need a transition away from both diesel and petrol engines, because both cause air pollution and climate change, so a scheme should only be made available if it does not incentivise a switch back from diesel to petrol, which would only take us in circles.
""The key principle must be to transition as quickly as possible away from all fossil-fuelled vehicles. "
A spokeswoman for the UK Government's Department for Environment, Food and Rural Affairs said: "The plan has not been published and I can't speculate on details."