In a statement the force said: "On Tuesday, April 23, at around 3.15pm, two girls aged 8 and 9 were on the playing fields near to the Recreation Ground, on Stainland Road.
"They were approached by a male with a dog.
"The male spoke to the girls and asked them if they wanted to play a game.
"The girls were frightened and ran out of the park and went straight home."
The incident was quickly reported to the police.
Police have described the suspect as a white male in his late teens, of skinny build with dark brown hair and a stubble beard.
They added he was wearing a black t-shirt and cream chinos.
The dog which was with him is described as a brown and ginger coloured dog with ginger ears on a pink lead.
The local neighbourhood team have been carrying out reassurance patrols in the area and are carrying out further enquiries.
Anyone who witnessed anything suspicious in the area or can provide any additional information is asked to contact 101.