It is understood the man may have been about to drive a train to Glasgow late on Wednesday night.
Industry sources said the man was thought to have been several times over the drink-drive limit and was led away in handcuffs by police. The man had been involved in coupling carriages together to form the 11:30pm train to Glasgow Queen Street.
British Transport Police (BTP) confirmed that a man had been arrested and may be the subject of a report to the procurator fiscal.
A BTP spokesman said: “At about 11:45pm on Wednesday, a 54-year-old man was arrested for allegedly being intoxicated while on duty as a train driver.”
The spokesman said BTP was awaiting the results of tests before sending a report to the procurator fiscal, relating to an offence under the Transport and Works Act.
A ScotRail spokeswoman said: “ScotRail is aware and will assist the BTP investigation in any way required as the safety of our customers and staff is of the utmost importance.”
The alleged incident comes six years after a ScotRail driver was jailed after drinking a bottle of whisky while on duty.