The AM Show host Duncan Garner says he's learned of a big site in the heart of downtown Auckland that will be used to create "hundreds" of affordable residences.
It's believed the build, once completed, will home as many people as the large-scale Hobsonville development in west Auckland.
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"We give [Housing Minister] Phil Twyford a lot of stick, don't we, for not building these homes," Garner said on Friday morning.
"But there's information I know as of right now. Phil Twyford and the Government have bought this big, massive block of land in Auckland CBD and they will be putting affordable homes on there.
"When I say homes I'm talking apartments. This will be a massive Sky Tower-type thing, a huge high-rise full of affordable homes.
"It could be hundreds and hundreds of apartments. There will be an announcement at some stage shortly from Phil Twyford, but not today."
Speaking on The AM Show earlier on Friday morning, Mr Twyford admitted he would be making an announcement about a land purchase in Auckland.
While he said he'd elaborate more on just what he was buying at a later time, he admitted it would be "big, believe me".
Mr Twyford has been approached for further comment.
His press secretary is denying Garner's claims, saying he has "extrapolated from the minister's comments".
She said there were no plans for a building in the CBD but the Government would have many land purchase announcements to come.
Labour's flagship KiwiBuild policy promises 100,000 new homes in 10 years with 50,000 of those in Auckland.
The Government has also vowed to build 16,000 homes within three years.
Last month, Labour made a move to address the country's housing shortage by placing a ban on foreigners buying existing homes.