Raymond Paterson, 63, was last seen outside his home on Balcarres Street, Morningside on Friday at around 8.45pm.
He is described as white, 5ft 8inches tall, slim to medium build with blue eyes, short grey hair and has a Glaswegian accent. Raymond regularly wears a safari jacket with combat trousers.
He has links to the West Highlands and he may have journeyed by train to the Bridge of Orchy/Glencoe area using the West Coast line. Police enquiries have also indicated that Raymond may have travelled to London by rail.
Anyone who can help police with their efforts to trace Raymond is asked to come forward.
Inspector Murray Tait said: “We are asking the public for their assistance in helping us trace Raymond so we can establish that he is safe and well.
“Through police enquiries we believe that he may have used the train and I would ask anyone who remembers seeing him to contact Police Scotland immediately on 101.”