The boys, believed to be in their mid-teens, brandished a large knife at two young girls near the playground on the park in Great Greens Lane at around midday on Monday (May 2).
The girls ran home and told their parents, who immediately reported the frightening encounter to police.
No arrests have been made at this stage, but Lancashire Police are investigating and urging anyone with information to get in touch.
A police spokesman said: “On May 2, at between 11.30am to 12.10pm, we received a report of two young males on the park in Clayton Brook and one has flashed a knife at two girls.
"This as you imagine is quite concerning and we are currently trying to ID the males involved.
"They are described as young teenagers in black clothing. One had a bubble jacket on.