Karen Buckley, 24, had been at Sanctuary nightclub on Dumbarton Road from about 23.45 on Saturday night.
At 01:00 she told friends she was going to the toilet but did not return or take her jacket.
She was then seen on CCTV talking to a man outside the club, before leaving and walking towards Church Street.
Police say the direction she was heading in was westwards along Dumbarton Road, away from the city centre.
Police are particularly keen to speak to the man seen in conversation with the 24-year-old, who they believe may be able to help with their inquiries.
He is described as being of a stocky build with dark hair and was wearing a white shirt and dark trousers.
Friends of the Glasgow Caledonian University student raised the alarm yesterday, saying it was "very out of character" for her not to return home.
Her parents have flown over from Cork in Ireland as they also believe her behaviour is unusual.
Inspector Gavin Smith said: "Karen had been drinking alcohol with her friends but they say she was not drunk and they are very worried about her.
"Her friends say she would always contact them by text or phone to let them know where she was and she doesn't appear to have contacted anyone.
"I would urge anyone who may have seen Karen at all on Saturday night into Sunday morning to get in touch with police on 101 with any information at all."
Miss Buckley is described as white, around 5ft to 5ft 2in (155-160cm) in height, with brown eyes and dark hair with long black curly hair extensions in.
She was said to be wearing an all in one black jump suit with red high heels and a black handbag when she disappeared. She speaks in an Irish accent.
She lives with three other student friends in a flat in Hill Street, Garnethill, Glasgow, and earlier on Saturday evening had drinks with friends in the flat before going to the nightclub.
Police have appealed for information in relation to a student who disappeared from a Glasgow nightclub after telling friends she was going to the toilet.