A full scene examination is underway in a bush area on Scenic Dr. The search is expected to take all day and the road is expected to be closed until 7pm on Sunday.
Officers said they could not yet confirm if Millane’s body had been found.
On Saturday evening, police announced they would charge a 26-year-old man with her murder.
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Millane, 22, from Essex in the United Kingdom, was last seen in central Auckland on December 1 and was reported missing on Wednesday.
They had previously been speaking to him over Millane’s disappearance. He will remain in police custody until Monday morning when he will appear at Auckland District Court.
News of the expected murder charge comes after police confirmed Millane’s disappearance was being treated as a homicide.
At a press conference on Saturday, Detective Inspector Scott Beard said police had gathered evidence, from CCTV footage and scene examinations at the CityLife Hotel on Queen St, that determined “Grace is no longer alive”.
Beard said they “still do not know where Grace is” but they were “determined to find her and return her to her family”.
Back home in Essex, church services will be held to remember Millane.
Father John Corbyn, of Our Lady of Good Counsel Roman Catholic Church in Wickford, where the Millane family lives said she was well known in the community.
“Many of our young people went to school with her. She went to Catholic school, and so did they, so they know her.
“We were praying for her while she was missing, and then of course … the sad realisation that she wasn’t missing any longer, as it were.”
He said the mood at the church was “rather sombre and sad”, adding: “I didn’t know her personally but many of the people here do. They’re shocked and saddened by what’s happened.”
Masses in Millane’s memory will be held on Sunday morning (UK time) where churchgoers would be “praying for her and her family”.
In Auckland, police continue to search the CityLife apartment where Millane was last seen at 9.41pm on December 1, and are sifting through hundreds of hours of CCTV footage.
They are also examining a “vehicle of interest”, which was seized on Saturday, and are trying to find out where it had recently travelled.
Beard said he had no evidence to suggest Millane knew the man before Saturday night but detectives knew they were together from the time she was captured on CCTV footage at SkyCity to the time she was seen at the CityLife Hotel.
Asked if the pair met on dating app Tinder, Beard said he would not speculate.
Detectives are still searching for some of Millane’s belongings, including her passport, a pale pink Casio Baby-G watch and a silver necklace with a green stone in the middle, which were missing from the Base Backpacker hostel where she was staying.
“That property is going to be somewhere, the clothing is going to be somewhere, we haven’t found it. Somebody may find it somewhere, we don’t know what has happened to it,” Beard said.
Police said the Millane’s family were “devastated” by the news her disappearance was being treated as a murder investigation.
Her father David Millane arrived in Auckland from Essex on Friday. Her brothers Michael and Declan Millane had been vocal in their search for their sister, urging people to share and retweet images of her online.
Millane was on a year-long OE after graduating from the University of Lincoln in September.
The advertising graduate and keen artist arrived in New Zealand on November 20, after travelling through South America.
This was her first time travelling abroad alone.