Nigel Poustie was taken to Ninewells Hospital after being found in Charleston Drive at about 18:30 on Monday, but died the following day.
Officers have carried out "extensive inquiries" into the circumstances surrounding Mr Poustie's death.
It is understood witnesses saw him fall several times.
Det Insp Brian Geddes said:  "Following information that we have obtained during this time, the circumstances surrounding his death are being treated as suspicious and as such, we continue to appeal for information to assist us with our enquiries."
Mr Poustie was wearing a dark jacket and black "tammy" hat with a red band when he was discovered.
Det Insp Geddes said officers wanted to speak to anyone who had contact with him on Monday.
He said: "During our inquiries we have spoken with members of Mr Poustie's family, his friends and neighbours, but we want make sure that we have contacted as many people as possible who may have known him."
The death of a 49-year-old man who was discovered seriously injured in a Dundee street is being treated as suspicious, police have confirmed.