The incident took place at 12.25am on Thursday 29th March after a 25-year-old man and 23-year-old woman used the ATM machine on the corner of Forrest Road and Lauriston Place.
Following use of the ATM, they were confronted by a man who threatened them with a glass bottle and demanded money.
The couple refused to hand over any money and the suspect then ran off towards George IV Bridge.
Officers are keen to speak with the man pictured in the CCTV footage as part of this ongoing investigation and anyone who recognises him is asked to come forward.
Detective Constable Iain Wallace from the Violence Reduction Unit at Gayfield Police Station said: “Fortunately, neither victim was injured or robbed of any money during this incident but we are treating the matter very seriously and are pursuing various lines of inquiry to trace the suspect.
“The man pictured is of interest to our investigation and anyone who can help us should contact police immediately.
“Similarly, anyone with any further information relevant to our ongoing inquiries is also urged to get in touch.”
Those with information can contact the VRU via 101 and quote incident number 151 of the 29th March 2018. Alternatively, an anonymous report can be made to the charity Crimestoppers on 0800 555 111.