John Scott only recently moved to the Falkirk area having lived previously in Glenboig.
The 37-year-old was last seen leaving the Royal Infirmary in Glasgow about 12.30pm last Tuesday, November 20.
Police officers believe that John left in his grey Hyundai i20 car and his destination is as yet unknown.
There have been no further confirmed sightings of him at this time.
As well as Glenboig, John also has links to the Pollok area of Glasgow and officers are continuing with their investigation within these areas, and Denny, to locate him.
Anyone who knows John’s current whereabouts is asked to come forward.
He is described as white, around 6ft tall with a medium build, short fair coloured hair, stubble. When last seen, he was wearing denim jeans, a grey jumper, black jacket and white baseball cap with a black skip.
Chief Inspector Damian Armstrong, local area commander for Falkirk, said: “It has now been an entire week since John left the Royal Infirmary in Glasgow and since this time he has not returned home, and there have been no further confirmed sightings of him.
“This is making not only us, but his family, increasingly concerned for his welfare and we are keen to trace him as soon as possible.
“John is likely to be travelling in his Hyndai i20 car, which has registration number SH11 FWX. We would urge anyone who has seen this vehicle since Tuesday, November 20, or who can help us establish its movements, to contact police immediately.
“We would also request that John get in touch as a matter of urgency to confirm he is safe.”
Those with information can contact Falkirk Police Station via 101 and quote incident number 3878 of November 21.