Officers are trying to track 47-year-old Richard Henderson, who was last seen in the Castle Street area of Glasgow at around 7.40pm on Saturday, May 3.
Police believe he may have travelled by bus towards the city centre.
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He is described as white, around 5ft 7in tall, of average build, with brown hair.
When last seen, he was wearing a distinctive black and red zip-up top, beige trousers, black trainers, and a light beige summer hat.
He was also carrying a black holdall and a blue/grey holdall.
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Sergeant Scott Gallacher, of Baird Street Police Office, said: “Extensive enquiries are ongoing to trace Richard and we are becoming concerned for his welfare.
“He has links to the Dumfries and Galloway area as well as Glasgow city centre.
“We are asking anyone who has seen him or knows where he might be to get in touch.
“We are also appealing directly to Richard – if you see this appeal, please let us know you are safe and well.”
Anyone with information is asked to contact police on 101, quoting incident 3412 of Saturday, May 3, 2025.