A tent set up over an entry point on the floor of the old Ashburton county building, and an extraction unit.
Contractors CleanTech have been on-site since last week.
Ashburton council finance and business support manager Paul Brake said initial scans showed an anomaly in the foundation, now understood to be pipework.
Any asbestos found in the enclosed area will be bagged, then the bags decontaminated, before removed from the site.
WorkSafe and specialist advisers have been involved.
The county building, garages behind it, and the nearby Methodist church hall, and the former Paul May building, have been demolished to make way for the council's new $51.6m civic and library building.
