Police Scotland said “extensive inquires” to trace the 52-year-old have failed to find him.
The force previously urged nearby residents to check any outhouses in case he had sought shelter there.
He is described as white, about 5ft 10ins, of average build and with short, grey hair.
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He was last seen wearing a work-style navy jacket, navy trousers, light blue shirt, navy tie and black shoes.
He may also be wearing a dark-coloured hat and carrying a rucksack.
On Friday, officers spoke to a number of people on Stanley Crescent, Crieff Road and Viewfield Place between 8.30pm and 9.30pm as part of their efforts to find him.
Inspector Duncan said: “In a bid to jog memories, we had officers out in the last known place John was, around the same time a week on.
“While continue our inquiries and assess any information gained, I would again urge anyone who may have seen John since Friday December 27, to please get in touch.”
Anyone with information is asked to contact 101 quoting incident number 1118 of December 29.