Roderick Nisbet was reported missing from the St Leonard’s area of Edinburgh on Wednesday, November 19.
The last confirmed sighting of the 52-year-old was in Wilmslow town centre on Friday, November 21.
He is descried as 6ft 4in tall, of medium build with a bald head. When last seen he was wearing a navy-blue puffer jacket.
He has links to the Berwick-upon-Tweed, Manchester and Cheshire areas.
Inspector Ash Sayer said: “Enquiries to locate Roderick are ongoing and we’re working with our colleagues across the country to find him.
“As part of our investigation we’re keen to hear from anyone who believes they may have seen him, or anyone who knows where he is at this time. The same goes for anyone with any CCTV or video footage of him.
“I would also like to appeal directly to Roderick and ask him to contact us directly to let us know he is safe ad well.”
Anyone with any information in relation to Roderick’s whereabouts is asked to call Cheshire Police on 101 quoting IML-2218562, information can also be reported online at www.cheshire.police.uk/tell-us .