Sarah Goldie, 18, was reported missing from her home in Renfrew on Friday night. Her bag was later found near to where a woman was seen in the water.
Police said officers from their specialist marine unit were continuing to search the River Clyde.
They also appealed for anyone with information to get in touch.
Police previously said that Ms Goldie left home at about 11:00 on Friday.
At about 18:00 she took a taxi from Glasgow to Renfrew, and was dropped off in Torridon Drive area.
About 19:40, police received a call about a young woman in the River Clyde near the Broomielaw and George V Bridge.
Emergency services including a helicopter began a search and two men entered the water, but the woman could not be found.
Ch Insp Mark Sutherland, of Police Scotland, said: "Our inquiry to trace Sarah Goldie continues and I would like to thank the public who have responded so positively to our appeals for information which has allowed us to speak to a number of significant witnesses.
"We have been piecing together Sarah's movements on Friday in both Renfrew and Glasgow through CCTV evidence and witness accounts.
"We have spoken to a number of people who witnessed an incident close to the King George V Bridge in Glasgow later that evening and now firmly believe that the young woman who was seen in the water is Sarah Goldie from the Renfrew area."
Ch Insp Sutherland added: "We have continued to keep Sarah's family updated throughout our inquiry.
"No-one else is believed to have been involved in the incident that led to Sarah entering the water.
"I would again like to thank everyone who took the time to contact police and would continue to ask that anyone with information about Sarah can contact Glasgow City Centre Police."
Ms Goldie is described as white, 5ft 6in tall, of medium build, with brown eyes and sandy/strawberry blond straight hair.
She was last seen wearing a khaki green Parka-type jacket with a fur hood and was carrying a cherry-red handbag.
Police have said for the first time that they believe a woman seen in the River Clyde in Glasgow was a missing teenager from Renfrewshire.