The operator is reportedly mulling the measure amid increasingly strict coronavirus rules in Scotland.
The move would be “welcomed” by railway staff who often have to deal with anti-social behaviour, according to trade union bosses.
“There has always been a concern with anti-social behaviour and assaults on staff, it's an ongoing issue,” Mick Hogg, regional organiser for the National Union of Rail, Maritime and Transport Workers, told the BBC.
”We certainly encourage our people to use the body cameras available in order to send a signal to people, and to report anti-social behaviour to the British Transport Police if it's serious.
“A total ban on alcohol is something we've been advocating for a number of years.”
According to Mr Hogg, train workers are still getting pushback from passengers about having to wear masks and adhere to social distancing guidelines.
He added that an alcohol ban, though welcome, would be difficult for Scotrail employees to enforce.
“We can only advise people they shouldn't be drinking and if that fails it's a matter for the BTP.
“We certainly welcome a ban but it really begs the question - who is going to police it?”
Scotrail confirmed to The Independent that an alcohol ban “is something they are looking into” but had no further details to share at this stage.
It follows the news that armed forces veterans can now apply for a railcard that will offer a 34 per cent discount on many train tickets for journeys from 5 November.
Captain Sir Tom Moore, who served in the Second World War and raised millions for charity during lockdown, was presented with the first Veterans Railcard to be issued.
The ninth national railcard is open to “UK veterans who served at least one day in Her Majesty’s Armed Forces or Merchant Mariners who have seen duty on legally defined military operations”. The Rail Delivery Group (RDG), which administers the scheme, estimates that 830,000 people will be eligible.