Detectives want to speak to the man over an incident in Chippingham Street, Attercliffe, in which a woman was approached by a man who initially asked for her telephone number.
When she refused to give it, the man touched her inappropriately over her clothing and attempted to kiss her.
The incident happened at around 3pm on Wednesday, August 23.
A South Yorkshire Police spokeswoman said: "A woman was walking along Chippingham Street, Attercliffe, towards the tram stop when she was reportedly approached by a man as she crossed on to a nearby bridge.
"The man asked for her phone number and when the woman declined, he reportedly touched her inappropriately over her clothing and tried to kiss her.
"The woman tried to leave, crossing over the bridge where she was then able to phone police. The man then left the area on foot.
"Officers have since been working with the victim to produce an E-fit image of the suspect and want to hear from anyone who thinks they may know who he is."
Call South Yorkshire Police on 101 or Crimestoppers on 0800 555111.