The 31-year-old was on a train travelling between Ibrox and Cessnock stations when he was approached by another man who made threats to him.
British Transport Police (BTP) has launched an investigation into the incident, which happened at around 5pm on Saturday, December 28.
The man they are looking for is though to be in his 30s.
No one was injured during the incident and officers have reviewed local closed-circuit television footage.
Constable Brian Kelly, the BTP officer in charge of the enquiry, is appealing for anyone with information to come forward.