Rufus Brickell, 22, was reported missing from the Dalry area of the city but CCTV footage shows him boarding a train from Glasgow Queen Street to Kilpatrick Station, just after midnight on Sunday October 6th.
The Herriot Watt University student, originally from Bristol, then left the station and walked south across the Erskine Bridge.
Officers are continuing to review CCTV footage and conduct door-to-door inquiries and specialist searches are being carried out near the bridge.
His family has now issued a further appeal in a bid to help trace Rufus.
It says: “Rufus has been missing for over a week now and we are completely shocked by his disappearance. We are so worried and desperate to know where he is.
“If Rufus sees this, we don’t want him to be concerned about being in any trouble. We just want him to know how much we love him and miss him and that we desperately want him home safe and well.
“We would ask that if anyone has seen Rufus since early Sunday morning, or saw him on the train he took to Kilpatrick station or walking over the Erskine bridge, to please phone the police and give them any information you have.
“We are extremely grateful to the police and those who have supported their enquiries in their efforts to trace Rufus. We would also like to thank everyone who has shared the social media appeals.”
Sergeant Kieran Dougal, leading the search, said: “After extensive enquiries, we have found clear CCTV footage of Rufus getting on and off the train to Kilpatrick station.
“Rufus is described as white, around 5ft 11ins in height and of muscular build with short brown hair. As the CCTV images show, he was last seen wearing a distinctive two-tone grey Berghaus jacket with a yellow patch on the back, black jeans that were rolled up at the bottom to reveal white socks, and black and white New Balance trainers. He was also carrying a navy blue rucksack with blue and red stripes at the bottom.
“We are continuing to urge anyone with information to come forward and we’d particularly ask anyone who was on the train and saw Rufus to contact us. We would also appeal to anyone in the Erskine bridge area at that time who may have dash-cam footage or who may have been cycling and have a ‘Go Pro’ camera to get in touch.
“Naturally Rufus’s family is extremely concerned and we just want to trace him as soon as possible to ensure he is safe."
Anyone with any information should contact police on 101 quoting reference 1477 of Sunday 6 October.