Officers were alerted to a man near a layby cafe on Newton Road, West Bromwich, at 12.30am on Monday.
A member of the public raised the alarm to police after chatting to the man, who said his name was Jake.
Jake said he suffered with mental health issues and wanted to die, West Midlands Police said. He then headed off towards Sandwell Valley Country Park.
The man has been described as white, around 21 years old, with long black hair. He was wearing joggers and a hoodie top.
A spokesman for West Midlands Police said: "We’ve searched the area using police dogs and our helicopter, but haven’t found anyone matching Jake’s description.
"We’re concerned and would like to find this man to make sure is okay. If you recognise anyone matching this vague description or know anyone who may be suffering with their mental health who could have been in the area at that time please get in touch."
Anyone who saw anything suspicious – or people who have dash-cam footage – should contact the Western Locate team on 01902 649150.