Ms Meagher was initially believed to have left Bar Etiquette in Brunswick about 1.30am (AEST) on Saturday, intending to make the short walk home and refusing a colleague's offer to accompany her.
But she then made a brief phone call to her brother Michael at the family's Perth home about 2am and police now say she may have stayed in the bar on busy Sydney Road.
Edith McKeon said her daughter had rushed home from holidaying in her native Ireland several weeks earlier after her father had a stroke.
'She rang Michael at about 2am on Saturday morning and she sounded worried and there were people in the background, and that's the last we've heard from her,' Mrs McKeon told Fairfax Media.
Michael told his sister he didn't want to wake their father.
'She just went I'm worried, I'm worried' and that really was the last bit of (contact),' Mrs McKeon said.
Ms Meagher then hung up, and Michael's repeated efforts to call her back failed, Mrs McKeon said.
Homicide squad head Detective Inspector John Potter said Ms Meagher and her brother had talked about their father's health.
'We are inclined to think what they were discussing was the health of the dad and the noise in the background was in fact the bar there, which leads us to believe that she stayed on in the bar longer than the last of her colleagues (who) had left, we understand, at about 1.30,' Det Insp Potter told ABC radio.