The man, said to be aged between 25 and 30, was seen near a property in Orchard Place, Livingston, West Lothian, in the early hours of Wednesday May 7.
He is described as being white, about 5ft 10in and of thin build. He has a long face, a large thin nose and short dark brown or black hair, and was wearing a grey sweatshirt.
Detective Superintendent Pat Campbell, of Police Scotland, said: "Can I stress that this male may have had legitimate reasons to be within this area at this time - and I would ask that if this is the case that the individual comes forward to the police in order to be eliminated from the investigation."
He asked that suggestions as to the man's identity be forwarded to the police as a matter of urgency. Members of the public are asked to call 101 with any information.