The attempted robbery happened at 7.45pm pm Friday, March 1 when a 24-year-old man was walking his pug in Elm Row.
Two men exited a white Transit van and attempted to steal the dog from the victim.
A struggle took place before the suspects were disturbed by the a passing motorist in a dark-coloured Peugeot 206.
Both suspects, described only as being white with stocky builds, then got back into their vehicle and drove off.
Officers are now urging anyone who can assist with this inquiry to come forward.
Detective Sergeant Callum Peoples from Galashiels CID said: “At this time, we are working to establish the full circumstances of this incident and would urge anyone who believes they have any relevant information to come forward.
“Similarly, if you were on Elm Row during Friday evening and witnessed what happened, or can help us identify the men responsible then please also contact police immediately.
“In particular, we are keen to speak to the driver, and any other occupants of the Peugeot 206, which passed this incident, but didn’t stop. These individuals are also urged to get in touch.”
Anyone with information can contact Galashiels CID via 101 and quote incident number 4251 of March 1. Alternatively, anonymous reports can be made to the Crimestoppers on 0800 555 111.
It comes a week after a Stirches man warned local dog owners to change their daily walking routing and keep to well lit areas, after believing he was followed when out with his parents’ shih tzu-Yorkshire terrier cross.
David Douglas said: “It looks like there are dogsnatchers operating in the Stirches area,
“Last Monday night I was walking my dog and a man seemed to be following me from the entrance to Roxburgh Drive round to Alemoor Court.
“I’ve also been getting followed by Crailing Court and round the back by Lanton Place.”
After posting the warning on social media, Mr Douglas said a number of people commented saying they had had similar experiences.
“I had no idea it was this widespread across the region,” he said.