Detectives are seeking assistance from the public following three incidents at parks in Mill Park and Lalor in April and June.
Investigators have been told a woman was walking alone on a football oval at Lalor Reserve when she observed an unknown man expose himself and perform a lewd act on April 15, about 12.50pm.
Two other women have come forward to police to report similar incidents at WA Smith Reserve in Lalor about 10.50am on June 7, and at Sycamore Reserve in Mill Park about 3.50pm on June 13.
The man is described as approximately 160cm tall, with a solid build and a dark-coloured beard.
Investigators believe the three incidents are linked and have released a computer-generated image of a man who may be able to assist with their inquiries.
Anyone with information that could assist police is urged to contact Crime Stoppers on 1800 333 000 or submit a confidential report online at www.crimestoppersvic.com.au.