The man, believed to be Michael, was recovered from the river this morning.
At around 9am police were called following reports of a body being found in the water near to the South Portland Street suspension bridge.
DNA tests are taking place to formally identify the body but the family believe it is the missing 23-year-old.
It came after a high profile campaign was launched to find Michael, who was reported missing when he did not return home from a night out.
As reported in the Evening Times, Michael from Dumbarton, West Dunbartonshire, left the Sugar Cube nightclub in Glasgow's Queen Street shortly after 2am last Friday.
CCTV images showed him in a Subway sandwich shop before acting erratically at around 2.30am in nearby St Enoch Square.
There were claims he had been seen at St Andrew's Cathedral in Clyde Street soon after.
Michael's dad John, 52, and mum Elaine, 53, said it was completely out of character for their sociable son to disappear.
Michael's uncle Vincent Slaven said the family were contacted by police today with the news that a body had been found. He said their worst fears had now come true.
"We believe the body to be Michael," he said. "He's wearing the same clothes that Michael was wearing when he went missing.
"They're doing DNA tests because of the length of time the body's been in the river.
"We always feared that the river was the most logical place he might be. We retraced his steps and found that he could only have gone a few ways.
"We were hoping he had gone into the Gorbals.
"Police are now looking at more CCTV pictures to try and piece together what happened."
Mr Slaven spoke on the behalf of the family to thank members of the public, family, Michael's friends shopkeepers and the press for helping them in trying to trace Michael's whereabouts.
He said: "The family would like to thank everyone for supporting us in trying to find Michael.
"We would like to thank the Herald and Times Group for helping us so early on and we thank the 300 volunteers for giving up their time and joining us in the search.
"It was heart warming for us to see the love towards Michael.
"John would also like to thank the local printers who printed the posters for no charge. We really have seen such human kindness."
A spokesman from Police Scotland said: "Police Scotland can confirm a body of a man was recovered from the River Clyde yesterday morning around 9am near the Suspension Bridge."