The hunt for the 32-year-old from Essex, who disappeared in Mt Aspiring National Park over the weekend, is continuing this morning with search and rescue teams using thermal imaging cameras and drones.
Ms Simpson's brother-in-law Sam Hazelton told Sky News the family were all worried and desperate for information.
"The New Zealand police have said there have been two sightings of her on the trail but we don't know the source of the information or have any further details."
Mr Hazelton said the last time the family heard from Stephanie was on WhatsApp early on Thursday morning.
"She contacted her friends after that on the Friday to say she was going hiking and camping.
"This was something Stephanie would do most weekends, it was her main reason for staying in Wanaka in New Zealand as it offered so many different trails.
"Stephanie is very competent and physically fit. She is relatively experienced in outdoor activities and has already completed a number of hikes. She is such a fun-loving, kind, determined and adventurous woman, we are asking anyone who might know anything to please get in touch with police," Hazelton told Sky News.
"It is a large search area and much of it is difficult terrain."
Police continue to appeal to hear from anyone who stayed in the Cameron Flat area on Friday and saw or spoke to Ms Simpson, or anyone who may have seen her in the area.
Yesterday, police said they were still optimistic they would find Ms Simpson.
Sergeant Mark Kirkwood, of Haast, in charge of the search operation, said overnight temperatures had not been cold, the rivers were not as high as recent levels and Simpson was "an experienced and very fit" tramper.
Ms Simpson was believed to have gone for a day hike to Brewster hut and had planned to walk to the glacier about 2km north of the hut.
She also planned to visit Blue Pools, near Makarora.
She was reported missing about 8.45am on Monday when she failed to keep an appointment.
Wanaka and West Coast search and rescue teams as well as members of the public began combing the trails from Fantail Falls to Mt Armstrong and in the Makarora Valley yesterday.
Sgt Kirkwood said Ms Simpson was carrying only a day pack and probably did not take a search and rescue beacon with her.
Ms Simpson arrived in Wanaka in November and has been working as a landscape gardener for Doug the Gardener.
- additional reporting by Kerrie Waterworth