Industry sources said the move is expected to be announced as part of the next phase of lockdown easing.
Demand for public transport is expected to increase, such as more shops are allowed to re-open.
ScotRail has already warned the currently recommended 2 metre distancing will not always be possible on its trains, even with their capacity reduced by as much as 80 per cent.
The development comes as Scottish Government-funded research is investigating how to double the carrying capacity of buses to 50 per cent, such as with screens between seats.
The move to compulsory face coverings follows First Minister Nicola Sturgeon announcing two weeks ago she would consider it.
That was triggered by anecdotal evidence that people were ignoring guidance that they should be worn in enclosed public spaces.
Ms Sturgeon said: “It is something we are considering and I think that is inevitable”.
The change of approach comes after transport secretary Michael Matheson previously stating that the move would be difficult to enforce.
It is not clear whether the measure will also apply to ferries, which have open deck areas available to passengers.
There was speculation it could be extended to shops, but it is understood that has been resisted by retailers.
Confirmation of compulsory face coverings on buses and trains would bring Scotland into line with England, where they have been mandatory since Monday.
Passengers on cross-Border trains have been encouraged to keep them on for the whole journey.
One public transport operator said: “As people come back to using public transport, it is to increase public confidence.”
'Another boost to safety measures’
Up to 70 per cent of Scots questioned in weekly polls by passenger watchdog Transport Focus have said they would only use buses and trains if people wore face coverings.
Paul White, director of the Confederation of Passenger Transport UK – Scotland, which represents bus and coach operators, said: “This is another boost to operators’ existing safety measures which are keeping buses safe for passengers and staff.
“Passengers have worked with bus operators and with each other to maintain social distancing guidelines.
“We will be looking to them to work with us to ensure the policy is a success.”
A spokesperson for the Scottish Government’s Transport Scotland agency, said: “Our advice is clear – a face covering should be worn when travelling on public transport unless you have a valid health reason not to do so.
“Work is ongoing across the Scottish Government and with stakeholders on the use of face coverings.
“We are also keeping any future need to make them mandatory under review.”
Meantime, Mr Matheson has funded Falkirk-based bus maker Alexander Dennis Limited (ADL) to investigate how vehicles could be adapted to carry “significantly” more passengers while keeping physically distanced.
Buses can currently accommodate only about a quarter of normal capacity, with some double deckers reduced to 18 passengers.
An industry source said: “The hope is that modifications will allow an increase in capacity to closer to 50 per cent.”
One bus operator told The Scotsman: “Plastic screen dividers on seats backs could be a way of upping capacity.”
Firms are also hoping the 2m physical distancing guidance will be halved to 1m to further increase numbers carried.
They pointed to some countries dropping physical distancing on public transport altogether.
Paul White of the Confederation of Passenger Transport said: “The safety of passengers and staff remains paramount.
“However, should a solution be identified that enhances Covid-19 protection while enabling buses to safely carry more passengers, this will greatly help the bus sector better meet growing travel demand through the relaxation of lockdown.”
A Transport Scotland spokesperson said: “We and Scottish Enterprise are supporting ADL, who are carrying out work to design and test ways of retrofitting bus interiors to enhance Covid-19 protection for both drivers and passengers.
“If a successful solution is found, either by ADL or other companies currently looking at protection measures, retrofitted buses may be able to operate at enhanced capacity while physical distancing rules are in place.”
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