Any information should be reported immediately by calling 111 and referencing file number 260707/5962, police said.
Police confirmed last week that the search had moved to a “limited search phase”.
“Once Police have thoroughly investigated the circumstances of a missing person and completed the available search tasks, it is normal to move into a limited search phase,” police said.
“This is a combination of reviewing what has already been done and identifying what tasks are still to be completed, as well as responding to any new information or lines of enquiry.
“While this is happening, the search operation is peer-reviewed, with a view to either suspend the search or complete any outstanding taskings.”
Police said over the last several days, they have reviewed CCTV of possible sightings and ensured all properties in the area have been cleared.
They said if they receive any new information about sightings or other evidence, it will be “assessed and any appropriate follow-up completed”.
Natalie, 80, left her Pōhara home on foot about 8.30am on July 6.
However, they said if no information comes to light, the search may be suspended.
“If there is no new information or tasks identified in the coming days, it is likely the search will be suspended.
“We are ensuring that Natalie’s family is kept updated.
“Our thoughts are with them at this extremely difficult time.”
Last week, a land and water search took place in Tākaka, utilising Land Search and Rescue teams, Surf Rescue inflatable rescue boats, drones, and Department of Conservation staff.