The fresh information followed a high-profile exhumation at Old Monkland Cemetery, Coatbridge, North Lanarkshire last month that failed to find Moira's body.
The investigation dates back to February 1957, when 11-year-old Moira disappeared in the town after catching a bus while on an errand. She is believed to have been abducted and murdered.
Recent reports have suggested detectives are now looking at the possibility Moira's remains may be in disused mineshafts under a housing estate following new witness evidence.
Police declined to comment on the details of the investigation, but said the mineshaft possibility was looked at when first raised by a television documentary some years ago.