Officers from West Midlands Police found the body in the woodland in Edgbaston after a week-long search for 33-year-old Jack.
Jack, who was from Handsworth and had links to Wolverhampton, had gone missing on July 29, with West Midlands Police saying at the time they were concerned for his welfare.
The force said that while formal identification had not yet taken place, Jack’s family had been informed, and offered sympathies to them and his friends at this time.
A spokesman for West Midlands Police said: “Officers searching for missing 33-year-old Jack have sadly found a body in woodland in Edgbaston.
“Formal identification is yet to take place but Jack’s family have been informed.
“We are not treating the death as suspicious and our sympathies are with his family and friends.”