The youngsters, aged 11-years-old, were walking through Wincobank Woods at about 3pm last Sunday, June 26 when a man approached them.
The man is said to have asked the two girls to follow him, police said, but they ran away after he allegedly pointed a knife at them.
Detectives are now investigating.
“While I appreciate incidents like this are alarming, I want to reassure you that this is a priority for us and we are doing everything we can to identify the man involved,” said Detective Constable Jonathan Kirkham as an appeal for information is issued today (Saturday, July 2).
“Following initial enquiries, which have included analysing CCTV footage of the area and house-to-house enquiries, we are now appealing for anyone who knows anything about the incident to come forward.
“He is described as white, in his early 20s, with long ginger hair which was tied back in a ponytail. He is thought to have been wearing a pale blue t-shirt which had drawings of female faces on.”
Anyone with information is asked to call South Yorkshire Police on 101, quoting reference 891 of June 26.