Police say they hope to interview in relation to the homicide later today.
Meanwhile, the two tourists were spoken to by police overnight. They remain in Christchurch Hospital in stable conditions.
Scene examinations in Christchurch and on the West Coast are continuing today.
The post-mortem examination on Ms Farrall's body, found in the boot of her car in a Woolston supermarket on Sunday, will continue today.
Police today continue to appeal for any sightings of the Nissan Terrano vehicle driven by the 38-year-old "person of interest", in the Christchurch area and between Christchurch and the West Coast on Saturday.
Sightings are also sought of Ms Farrall's white Toyota Corolla in the Woolston area on Saturday morning
Police hope to release a photograph of the Nissan Terrano vehicle later today.
Ms Farrall, a community support worker, had been reported missing by an acquaintance on Saturday afternoon.
Police say it was too early to say how or where the 24-year-old was killed.
Anyone with information about the vehicles or any other aspects of the case is asked to contact Christchurch police on 03 363 7400 or anonymously through Crimestoppers on 0800 555 111.
Ms Farrall's distraught family released a statement yesterday, saying she was a kind and caring girl who loved animals.
She worked as a caregiver for Richmond Fellowship in Christchurch and her family said she was always helping people in need.
"As a family we are devastated that her caring nature appears to have been tragically taken advantage of," they said in a statement.
The police believe the car had been at the supermarket since around 10am on Saturday.
Amy had spoken to people early on Saturday morning, and the 38-year-old man "was mentioned", Mr Fitzgerald confirmed.
Police are not seeking anyone else in the investigation.
Tourists shocked by brutal attack
Tourists backpacking around the beauty spots of the South Island's wild West Coast have been shocked by the brutal attack on two young women.
But opinion is divided on whether they should continue hitchhiking, with some vowing to give up the risky practice and others saying they're not deterred by the one-off event.
A 28-year-old German woman and a 27-year-old Japanese woman were attacked after hitching a ride near Franz Josef on Sunday.
One woman was stabbed and the other one was badly injured after being dumped from the moving vehicle like "a bag of rubbish", according to eye-witnesses.
Meanwhile, the attack has shocked the backpacker community.
Annika Kroll, from Germany, has been travelling around New Zealand since December.
The 18-year-old had planned to hitchhike from Greymouth to Te Anau in the next few days to attempt the Milford Track in Fiordland National Park. But she had been shaken up by Sunday's events.
"You hear lovely stories about people hitchhiking in New Zealand and meeting amazing people, and how it's such a safe place," she said, speaking at the Duke Hostel in Greymouth.
"This is unexpected and very shocking, and I don't think I can hitchhike any more.
"And I won't be telling my mother [back in Germany] about this. She will worry too much."
Last year, a coroner highlighted the risks involved in hitchhiking after Czech tourist Dagmar Pytlickova, 31, was picked up by convicted kidnapper Jason Frandi before he sexually assaulted and killed her.
During the hearing, police revealed there was no official police policy on hitchhiking, but they warned against doing it.
Some tourists are putting Sunday's attack down as a tragic, one-off event and have vowed to continue thumbing rides.
Ann Scott, manager of Ivory Towers lodge and backpackers at Fox Glacier, said plenty of tourists were on the road hitching yesterday.
"They were all pretty nonplussed about it," she said.
"As dreadful as it is for the two girls and their families, it's the risk you take when you're hitching."
Hitchhiking is a popular way of getting up and down the West Coast.
Jan Hartlieb, an 18-year-old German, said he would still hitchhike alone but would be more cautious.
Even a 22-year-old Israeli woman, who did not want to be named, said she had hitchhiked from Franz Josef to Greymouth on Sunday - the same day as the attack - but vowed to continue thumbing for lifts.
"I felt very upset and shocked that it happened the same day I was hitchhiking but I will still do it. There are not many options."
