New Zealand Police said a 26-year-old man has been speaking with officers in Auckland in relation to the disappearance of the 22-year-old, who went missing from a hostel in Auckland on December 1. "We are determined to find her and return her to her family".
"Just after 3pm this afternoon a 26-year-old man was located at a central Auckland address by police", Detective Inspector Scott Beard told media.
The 26-year-old is the same man who was questioned previously by police and was with Ms Millane at several places, including Sky City, before going to CityLife Hotel with her.
David Millane arrived in New Zealand on Friday morning, after the family raised the alert earlier in the week, having not heard from Grace since Saturday (December 1) - which he said was unusual.
Grace was last seen wearing a black dress with white sneakers on Queen Street, in Auckland's CBD, at around 9.41pm last Saturday.
Detectives said yesterday they were continuing to view hundreds of hours of CCTV footage, while they continue to examine the CityLife Hotel in central Auckland, where she was last seen entering with a man on Saturday night.
He added: "I know that the thoughts of all New Zealanders will be with Grace's family tonight".
Millane was on a year-long OE after graduating from the University of Lincoln in September.
Her passport is also missing.
"The issue here is Grace is still missing and we want to find her".
"I want to reassure everyone, both here and overseas, that New Zealand Police are determined to do everything we can to find her".
"He was brought back to the Auckland Central Police Station and is now speaking to us in relation to the murder of Grace Millane".
Members of Millane's family have made appeals on Facebook for information.
Earlier on Saturday police released images of her necklace and watch and urged anyone who recognised the items to come forward.
Beard said "that property is going to be somewhere, the clothing is going to be somewhere, we haven't found it".
Police said they had received dozens of calls to a hotline and more than 25 staff were working on the case, trawling through hours of CCTV footage to trace her movements.
The man was with her on Saturday evening, but Beard didn't know if the pair knew each other before then.
Ms Millane, from Essex, was described as a "lovely, outgoing, fun-loving, family-orientated daughter" by her father, David Millane.
"Grace's family has been advised of this development and they are devastated".
He tearfully explained that his daughter has never been out of contact with her family for such a long period of time, usually contacting them on social media.