The girl was on the footpath between Scotties Bar and Craigentinny Cemetery at around 12:30pm, when a man approached and placed his hands on her shoulder, trying to make her go with him.
A passing woman became concerned, and intervened, and the man then ran off.
Detectives are keen to trace the woman as she may be have vital information that would help them find the man.
She is described as being white, in her mid-to-late 30s, with blonde hair tied back in a ponytail. She was wearing a black jacket, a luminous pink top, tight blue jeans, silver ballet pumps and was carrying a black handbag.
The suspect is white, in his mid-to-late 40s, with a hoop earring in his left ear and a bald head. He was carrying a dark green bottle.