The man was found collapsed near a shop in Great Bridge at around 6.30pm on April 15.
West Midlands Police and West Midlands Ambulance Service attended but the man was pronounced dead at the scene.
Police believe he may have been sleeping rough in a nearby outbuilding.
Officers have not be able to identify the man, who is described as white, aged approximately 40 years old and may be Polish.
His death is currently being treated as unexplained and a number of specialist forensic opportunities to identify him are being explored by police.
Detective Inspector Adam Jobson, from West Midlands Police's homicide team, said: "We really need your help to identify this man as we have not been able to make contact with his next of kin and loved ones.
“We feel sure that someone within the local community will know who he is, you may have previously seen him in the area.
“I am also appealing to anyone who may have seen something on or around the days leading up to the April 15.
“If you have any information, not matter how insignificant it may seem, please get in touch."
He added: “We are desperately trying to establish this man’s identity so we can contact his family and determine exactly what happened.
“A man has lost his life and we are sure people within the community know him or may have information about how he died. His family deserve to know, so if you can help us, please do."
Anyone with information that might help identify the man is urged to call West Midlands Police on 101, quoting log number 3880 of April 15.