The 23-year-old was standing at a bus stop on Easterhouse Road, near the junction with Aberdalgie Road, at around 9.25am on Monday, June 21, when a man approached her asking if he could borrow her mobile phone.
He then tried to steal the phone along with her handbag before running away towards the footpath near Denmilne Street.
The suspect has been described as a white man in his 40s, and who spoke with an Ayrshire accent.
He is roughly 5ft 5in tall, slim and has short, dark blonde hair and facial hair.
He was wearing black trousers, a black hooded jumper and black trainers.
Detective Constable Poppy Stewart, of Glasgow's Robbery Unit, said: "The victim is heavily pregnant and was thankfully not injured during what must have been a distressing incident for her.
"I am appealing to anyone who was in the Easterhouse Road area around 9.25am this morning and witnessed the attempted robbery or saw a male suspect matching this description to get in touch.
"If you were driving in the area and have a dash-cam, please check back and see if there is any footage that could assist our investigation."
If you have information on the incident you should call police on 101, quoting incident number 0730 of June 21. If you have information but would like to remain anonymous you can contact Crimestoppers on 0800 555 222.