William Etilage, who is 43, left home at around 10am on Friday 10 December 2021 and has not been seen since.
He was seen at a betting stop in Whitstable High Street the same day he went missing and officers are currently reviewing CCTV in an effort to locate him.
Mr Etilage has a strong Scottish accent and when he was last seen he was wearing jeans and a black Superdry coat.
Inspector Mark Sankey of Kent Police said: ‘We are very concerned for Mr Etilage’s wellbeing and want to stress that he is not in any trouble, we just want to know he is safe and well.’
Anyone with information is asked to call 101 quoting reference 10-1024.