Neil Molloy (69) was last seen boarding the number six bus at Forth Valley Royal Hospital in Larbert bound for Falkirk Bus Station at around 1.45pm last Thursday.
It is thought he got off in Main Street, Bainsford, at around 2.10pm and, although he has not been heard from since, it is now believed he may have been on Larbert Road, near to Bonnybridge Golf Club, around 5.50am on Friday.
Police are carrying out inquiries in the area in an effort to trace him.
Mr Molloy is 5ft 10in tall, average build, with a local accent. He has silver-framed glasses and was last seen wearing grey trousers, a light grey jacket and a white shirt.
Inspector Adrian Wright said: “We are keen to find Neil as quickly as possible and I’d urge anyone who has seen him or has information that can help us with our inquiries to please come forward immediately.”
Those with information can contact police on 101 or speak to any officer.