The 27-year-old remains in custody having been arrested on Saturday, 25 September.
An investigation was launched after police were called to reports of a man found injured outside Belvedere Railway Station at 10.13pm on Saturday, 18 September.
Despite the efforts of emergency services, Vitali Skrypniak, who was aged 45 and from Lviv Oblast in Ukraine, died at the scene.
A post-mortem examination held on Tuesday, 21 September at the Princess Royal University Hospital gave cause of death as a single stab wound to the chest.
Mr Skrypniak’s family have been told about the development and continue to be supported by specially trained officers.
Anyone with information about the incident is asked to call investigation room on 0208 345 3715. Alternatively call 101 quoting CAD 7975/18Sep.
To remain anonymous contact the independent charity Crimestoppers on 0800 555 111.