Officers said they have "drawn a blank" since finding the body in woodland off Peartree Avenue, Southampton, on Monday.
The man was wearing a sweatshirt from Zimbabwe, Hampshire Constabulary said.
He also had a tattoo on his upper right arm, drawn in "blue/black" ink, of an eagle's head with its mouth wide open.
The man was 6ft 3in (1.9m) tall, of "proportionate build", aged between 40 and 60, with a full head of greying hair.
His sweatshirt, described by police as grey, sports a badge showing a bird next to the words Mahenye Safari Lodge, Cona-re-zhou, Zimbabwe.
He was also wearing tracksuit bottoms bearing a Monster logo, and a pair of trainers.
It has not been possible to determine the man's ethnicity, and he does not match the description of anyone reported missing, the force said.
Launching an appeal for the public's help, Det Con Mark Blake said: "We are hoping that someone must know who this man is - someone must be missing him.
"He could be from anywhere, we just don't know."
An unusual sweatshirt logo and "distinctive" tattoo could hold the key to a dead man's identity - after police were unable to establish who he was.