Officers from Police Scotland's Major Investments Team are investigating the mysterious death of 41-year-old Scott McGuire.
It is believed he may have suffered a head
injury before he ended up in the water and police pledged to investigate any new information.
Mr McGuire, of Hutton Drive, in Govan, was found in the river in Glasgow city centre. Detectives are also looking into a report of a fire underneath the suspension bridge on July 8.
A Police Scotland spokeswoman said: "If anyone has any information to suggest Mr McGuire received injuries before he entered the water, we would urge them to contact officers.
"Any information we received will be passed to officers investigating his death. We would still appeal for any witnesses to contact Police Scotland."
As previously reported by the Evening Times, Mr McGuire's body was pulled from the water near Clyde Street last Tuesday.
Despite a post mortem examination, his death is being treated as "unexplained" and police are to carry out further forensic examinations.
Detective Inspector Martin Fergus, who is leading the inquiry, said: "We're trying to piece together the last movements of Scott, and our inquiries are progressing. However, I am looking for the assistance of the local community.
"Our inquiries have revealed that Scott had been sleeping rough near to where his body was later discovered, near to Carlton Place.
"There had been a report of a rubbish fire underneath the suspension bridge at around 5.30am on July 8.
"I would like to speak to anyone who was nearby around the time and remembers witnessing smoke."
Anyone with any information is asked to contact Police Scotland on 101.