A post mortem examination revealed he had numerous injuries.
“We’re still very early in the investigation, but they are significant injuries,” Detective Senior Sergeant Tom Mills said.
“The injuries give rise to our concerns in relation to the cause of his death.”
Police said the man travelled from Fremantle to Perth on Friday night and spent Saturday moving around the CBD.
The man is known to police but his photograph has not been released as his family has not been notified of his death.
The man was wearing a green, blue and grey checked zip-up hoodie, a light blue T-shirt with a palm tree motif and ‘California’ written on it, black jeans and white runners.
He had a black scarf wrapped around his neck and was carrying a blue sleeping bag and a blue child’s doona that had images of police cars, a tow truck and fire engines on one side, and yellow stars and dots on the other side.
Anyone who saw the man or was driving along Beaufort Street on Saturday night is urged to contact police.