Anyone who was on the Union Canal towpath between Hallglen and Polmont around 2-3pm last Saturday, September 5 and may have seen anything is asked to get in touch.
Officers are trying to identify a man who they suspect was on the towpath at the time.
He is described as white, slim build, around 5ft 6ins and with a local accent.
He was wearing a black hooded jacket, black tracksuit bottoms, black Nike trainers and carrying a black backpack.
A spokesperson for Falkirk Police said: “We're appealing for witnesses after a suspicious incident at the canal towpath.
“Can you help us identify a male who may have been on the towpath at that time?”
Anyone with information, or witnessed anything in relation to this incident, is asked to call 101, quoting reference 2387 of September 7.