Officers were alerted by a member of the public to concerning behaviour at around 6.45pm on Tuesday, June 20, at the playpark at Upperboat Road.
The man, who was in his 60s, approached and spoke to two children before leaving towards the Esslemont Drive park exit.
DC Liam McEwan said: "I must stress that no one was harmed in any way, however a member of the public who saw the man approach the two youngsters was concerned about his behaviour. We would like to establish the full circumstances of what happened and would urge this man if he recognises himself as being the person concerned to get in touch with Police.
"Likewise I would also ask that anyone who recognises the description provided or has information to call 101 quoting incident number 3821 of June 20 or Crimestoppers on 0800 555111 if you would prefer to remain anonymous."
The man is described as being of Asian appearance, between 5ft 2 and 5ft 4 in height, of a large build with facial stubble and short speckled grey/black hair with distinct patches on the left side which were either bald or grey.
He was wearing baggy grey trousers, grey plimsole shoes with a white rim, a black leather coat which was either buttoned or zipped up to the neck and numerous large gold rings on his hand.