The man was seen by a 30-year-old woman who was walking her dog on the canal path near to Alloway Grove - known locally as the Pipey - in Kirkintilloch.
She alerted police after the incident which happened on Wednesday at 6pm.
The man is described as white and around 5ft 8in with a pale complexion. He was in his late teens to early twenties and was wearing a dark hooded top.
He had a black coloured Alsatian type dog with him.
Detectives have urged anyone with information to call 101.