The 51-year-old victim was walking outside Hampden Park stadium towards Somerville Drive in the south side of Glasgow at around 12.30am on Sunday December 8 when she was approached by the man who later attacked her.
She needed hospital treatment for facial injuries she sustained and has been left traumatised, police said.
Officers have been reviewing CCTV footage and believe the man responsible had been at a Christmas party inside Hampden.
He is aged around 30, 5ft 10in to 6ft and has a medium build with short, dark hair. He was wearing a dark three-quarter length coat with white or cream buttons, a dark suit and a light shirt.
Police particularly want to speak to a man who gave the suspect directions as he left the party.
Detective Inspector Kate Jamieson of the National Rape Task Force said: "From studying CCTV, we believe that the suspect came out of the main entrance to Hampden Stadium just before midnight and engaged another man from the party night in conversation and it appears that he may have provided the suspect with directions.
"The other man is then seen returning inside to the party night. Extensive inquiries are ongoing to identify the suspect, and we will trace this man, but I would appreciate any information from others who were at the Christmas party night who may know the man responsible, or recognise the description.
"I would also like to urgently trace the man who provided directions to the suspect. Please don't wait for the police to come to you; do the right thing and come forward as you could hold that vital piece of information which could help lead us to whoever is responsible for this terrible crime."
Extra police patrols are been carried out in the Mount Florida area and police asked anyone with information to contact them on 101, or anonymously via Crimestoppers on 0800 555 111.