The incident happened at a play park near Ambrose Rise in the Dedridge area at about 04:15 on Friday.
The man, who was of Indian, Pakistani or Bangladeshi appearance, made off towards St Ninian's School.
The girl, who was not hurt, went home and told her parents who contacted police.
The suspect was 18-20-years-old, and about 5ft 10in. He was wearing a light-grey hooded top, grey skinny jeans and spoke with a Scottish accent.
Det Sgt Graham Garvie, from Livingston CID, said: "At this time we are trying to establish exactly what took place during this exchange and would ask anyone who was in the area and saw anything suspicious to contact police immediately.
"The young girl has given us a good description of the male we are looking to trace and anyone who recognises him should also get in touch."
A nine-year-old girl has been approached by a man in Livingston, who started talking to the child and tried to put his hands on her.