Kevin McFadden, 32, is described as "vulnerable" because he relies on daily medication, which he does not have with him.
He was last seen near St Andrew's Cathedral, in Clyde Street, about 6.30pm on August 4.
Mr McFadden, who is known to sleep rough in the West End and city centre, is about 6ft, of slim build and has receding brown hair.
Constable Graeme Waite said: "Although Kevin has a relatively transient lifestyle, he usually makes contact with his family."
Anyone with information is asked to call police on 101.