The incident happened at a property in the Robroyston area at about 11.45pm on Tuesday.
"Definite Line Of Inquiry" In Teen Rape
Police investigating the rape of a 14-year-old girl who was forced into bushes outside a supermarket are following a "definite line of inquiry''.
The victim was going to collect her bicycle after visiting an Asda store in Barrhead, East Renfrewshire, when she was attacked.
The man, who wore a white trilby-style hat, struck outside the town's Main Street Shopping Centre at about 8.15pm on Sunday.
Police Scotland said officers are following a "definite line of inquiry''.
Detective Inspector Gillian Patrick, from Police Scotland, said: "This was a particularly traumatic experience for the young girl concerned, who had been out in the local area before being attacked.
"I would like to reassure the local community that we are continuing extensive inquiries into this incident.
"We know the man was in the shop prior to the incident taking place and I am appealing to anyone who may have been shopping around that time to think about whether they may have seen this man or noticed anything suspicious.
"If you have any information or knowledge about this crime, please talk to officers and pass it on - it could prove vital in helping us trace the man responsible for this attack.''
The suspect is described as 20 to 30 and of medium build. He wore a grey zip top with white striped sleeves, grey jogging bottoms and grey trainers. He was carrying a black holdall.
Ms Patrick said: "I'm aware this incident will be of concern to people and I would like to confirm that additional patrols will be in the area to offer reassurance to local people and if anyone has any concerns, please speak to officers.''
Aileen Campbell pledged the Scottish Government will bring forward legislation after 82% of those who took part in a consultation backed the change.
Police Scotland's nationwide campaign will work to reduce alcohol-related attacks, weapon use and anti-social behaviour.
Passengers reported long queues in the terminal building and pictures on social media showed the security hall in near darkness.
Most Viewed Pictures On Heart
Recently Played Tracks
To listen live, choose your preferred station:
Now playing: The best feel good music
Deposit £10 to get a £40 Welcome Bonus - That's £50 to play bingo, slots and more!*
Over 50 tracks to make you feel-good. New album out now...
Find your local four day weather report here.
Make Heart the soundtrack to your day and you could be a winner with great prizes up for grabs throughout the day.
Find out more about some of the companies advertising on Heart Scotland- East.