Michael Errington, from Darlington, was last seen in his home town on Saturday morning but has not been seen since.
Officers searching for Mr Errington have now extended their search to Scotland where he has links.
A statement from Durham Constabulary said: “We are warning members of the public not to approach a missing Darlington man.”
Edinburgh police shared the full appeal from Durham Constabulary on social media and posted: “Our colleagues from Durham Constabulary believe missing Darlington man Michael Errington (51) may have travelled to Edinburgh.
“If you see him you should call Durham Police via 101 immediately.”
Mr Errington is described as being around 6ft tall, of medium build, bald, with tattoos on his arms and legs.
He was wearing a red polo shirt and may also be wearing a black jacket, blue jeans and white trainers.
Police have released an image of Michael, although he has lost a significant amount of weight since the photo was taken.
Acting Superintendent Steve Long, of Durham Constabulary, said: “We are appealing for anyone who has any information regarding Michael’s whereabouts to contact us.
“If members of the public do see him, we would urge them not to approach him but to call us immediately on 101.”
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