He targeted a woman walking along Chippingham Street, Attercliffe, at 3pm on Wednesday, August 23.
South Yorkshire Police said he asked for the woman's phone number, touched her over her clothing and tried to kiss her.
The attacker was Asian, between 18 and 20 years old, around 5ft 7ins, slim and had short, black hair.
He was wearing rectangular thin-framed glasses and traditional Asian style clothing in electric blue.
A South Yorkshire Police spokeswoman said: "Police in Sheffield are appealing for information after a woman was reportedly sexually assaulted while walking to work.
"At around 3pm on Wednesday, August 23, it is reported that a woman was walking along Chippingham Street in Attercliffe towards the tram stop when she was approached by an unknown man as she crossed onto a nearby bridge.
"The man asked for her phone number and when the woman declined, he touched her inappropriately over her clothing and tried to kiss her.
"The victim attempted to leave, crossing over the bridge, before being able to phone police, which prompted the offender to leave the scene on foot.
"Were you in the area between 3pm and 4pm? Were you waiting at the tram stop on Attercliffe Road? Did you see anything suspicious?"
Anyone with information should call South Yorkshire Police on 101.