On Facebook, Mrs Adams said her parents were flying from the UK and due to land in Christchurch tomorrow morning before being transferred to Hokitika.
Mr Bennett, who had been on a working holiday in New Zealand for three weeks, was lightly clad and only carrying a day pack when he went for a walk in the park, south of Greymouth on the west coast of the South Island.
Two helicopters and 15 ground searchers are involved in the search.
West Coast area commander Inspector Mel Aitken said: "Helicopters with heat-seeking devices and committed ground teams with a huge amount of expertise are involved in this search.
"Our thoughts are with the family at this time, as we continue our best efforts to reach a positive conclusion to this rescue."