Scott McGuire, 41, was found dead in the River Clyde in Glasgow at around 8.15am on Tuesday.
Police said his home address is Hutton Drive in the city but that he had been sleeping rough near a bridge that crosses the river at Calton Place.
There was a rubbish fire under the bridge shortly before Mr McGuire's body was found. Police are not linking it to the death but want to speak to anyone who was in the area at the time.
Officers are trying to establish the 41-year-old's final movements and know that he was at the Glasgow City Mission drop in centre close to Clyde Street on Monday evening.
Detective Inspector Martin Fergus said: "Our enquiries have revealed that Scott had been sleeping rough near to where his body was later discovered, near to Calton Place. There had been a report of a rubbish fire underneath the suspension bridge around 05.30am on July 8.
"Although at this time we do not believe that the fire is linked to Scott's death, I would like to speak to anyone who was nearby around the time of 05.30am and remembers witnessing smoke coming from near the suspension bridge.
"The fire service were in attendance, and we are hoping that this may jog the memories of people who were nearby. They may have information that could assist with our enquiry.
"We're continuing enquiries into the circumstances I would like to speak to anyone who can tell us of Scott's movements between the hours of 9.30pm on Monday July 7 when we know he was at the Mission drop inn centre, on Clyde Street, and 8.15am, when his body was discovered.
"I would particularly like to speak to anyone who may have witnessed anyone at or around the suspension Bridge and around the area of Calton Place between the hours of 4am and 8.15am."