The latest approach was towards a 10-year-old boy in the Harryville district of Ballymena.
However, the quick thinking child ran away to a nearby house to raise the alarm.
The PSNI say was not physically hurt but was left “badly shaken.”
Inspector Trevor Atkinson said: “The man is described as having dark hair and wearing a dark coat and was driving a large light coloured van,” he said.
“I would appeal to anyone who may have witnessed this incident or who has any information to contact Police at Ballymena on the non-emergency number 101.
“Or, if someone would prefer to provide information, without giving their details they can contact the independent charity Crimestoppers and speak to them anonymously on 0800 555 111.”
On St Patrick’s Day, Tuesday, March 17, a child was approached in Broughshane.
The approach was made as the ten year old boy walked along Braidwater Gardens at around 2:30 pm.
The man offered the child a sweet then grabbed him by the wrist.
The child kicked back and ran away.
The spokesperson added: “Thankfully the boy suffered no physically injury as a result. He was obviously very frightened by the incident.
“The man involved is described as tall with long dark hair, a small amount of facial hair and a cut on his left ear.
“He was wearing a black cap, dark glasses, a dark green coat and brown shoes.
“Police are making full efforts to locate this man and are asking for community support.
“This means bringing any relevant information to police on the non emergency 101 number.”