The remains were found in suitcases that had been sold to a Manurewa family as part of an auction to clear the storage locker last week, according to Newshub.
"I feel sorry for the family because they've got nothing to do with it. And whoever did do it, come on, front up. It's a bit unfair, bro. It's horrific, f***ing scary," a Manurewa neighbour, Shelton Honana, told Newshub.
The TV report said a police source had told them there might be multiple victims involved, but police won't confirm any details of the report.
Police launched a homicide investigation last week after the remains were found at a property on Moncreiff Ave in the suburb of Clendon Park.
Police have earlier said the occupants of the address were not believed to be involved in the homicide.
Newshub reported that the trailer-load of property was picked up from the storage unit after a family won an auction for items that had been left abandoned.
The remains were then reportedly found in suitcases after they were transported to the family's home. Newshub also reported, citing police sources, that the human remains may be from multiple victims.
In a statement last week, Detective Inspector Tofilau Faamanuia Vaaelua said last week that the discovery was made after the occupants, who are not believed to be involved, took "unowned property" to their address.
In a statement to the Herald, a police spokesperson would not confirm media reports.
"Given this is a homicide investigation, the flow of information into the public arena via media needs to be accurate and responsible."
Any errors in this space could compromise the investigation and might hinder the ability to hold a person or persons to account, the spokesperson said.
"As we've previously said, we appreciate there is a large public interest, however, there are still a number of inquiries to be carried out before police can comment further.
"The priority for police is to confirm the identification of the deceased so that we can establish the full circumstances behind the discovery.
"However, we are still awaiting the completion and results of the post-mortem examination so we are unable to comment," the spokesperson said.
"There is an expectation that actions by the media are equally accurate, responsible and lawful.
"Innocent people and families of victims should not be re-victimised or suffer undue stress by inaccurate or reckless reporting. Police will endeavour to provide media with an update as soon as we can."
