The man who was seen with missing student Karen Buckley outside the nightclub is now helping police with their inquiries.
They are now treating the incident as a high risk missing persons case.
Just about 30 minutes ago it was reported that her handbag had been found in Dawsholm Park near Maryhill.
And the police are now keen to trace the driver of a grey/silver car which was seen in country roads between Milngavie and Drymen between 11am and 3pm on Monday.
The police are asking if anyone saw the car maybe parked in a lay-by or on the road or any suspicious activity surrounding it.
At the police press conference this afternoon, Karen’s mum said: “We are desperate, she is our only daughter, we love her dearly. If anybody knows anything come forward.”
Detective Superintendent Jim Kerr, the officer leading the enquiry, said: “The man she was seen with on CCTV walking along Dumbarton Road after she left the club is now assisting us with our enquiries. I must stress that at this time he is not a suspect; from what we can see she does not appear under duress - there is no sign of struggle or reluctance on her part to leave the club, however, again that does not mean that nothing untoward has happened to her.
“There was talk of another man she had been seen with – we have also spoken to him – so we are no longer trying to trace either of them. However we do need the public to come forward with any information they may have. To them it may seem insignificant, however, to us it may be the piece of information that leads to us finding her.
“We need information about her whereabouts and her movements after leaving the club.”
He added: “Karen is a lovely girl, close to her family and popular with her friends. She has only been in Glasgow a few months, and if staying out will always let her friends know – hence the real concern here. Like all youngsters, she is also very active on social media but there has been no activity on any of her accounts since Saturday night early Sunday morning.”
Karen (24) from Cork in Ireland, was last seen walking away from a nightclub in Glasgow’s west end after talking to a man outside.
The Glasgow Caledonian University student had been at Sanctuary nightclub on Dumbarton Road from about 11.45pm on Saturday night.
At about 1am she told friends she was going to the toilet but she didn’t come back and didn’t pick up her jacket.
CCTV cameras captured images of her talking to a man outside the club, then she left and walked towards Church Street.
Miss Buckley is described as white, about 5ft to 5ft 2in (155-160cm) tall, 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.
An incident room has been set up at Govan police office – anyone with information is asked to call officers via the 101 number and ask for the incident room. Information can also be passed in confidence to Crimestoppers on 0800 555 111.