One of the pieces - 133-year-old Chief Ngatai-Raure portrait – purportedly surfaced for sale on the dark web late last year.
But art crime experts spoken to by the Herald have analysed the listing, which had a buy-now price of nearly $1m, payable in bitcoin, and declared it a fake.
It's possible that the Lindauers were whisked overseas for on-sale, according to the world's top art sleuth Christopher Marinello, but he also warned there's a chance they could still be hidden in New Zealand.
"Usually, thieves try to 'cash out' as quickly as possible," said the London-based art detective who helped recover a billion-dollar horde of Nazi loot in Munich in 2012.
"The relatively quick response by the police and media rendered these paintings radioactive or unable to sell openly. There is always a market for stolen goods on the black market at a fraction of their true value.
"It is possible that these were smuggled out of New Zealand once the press coverage took over but moving stolen artwork is always risky and these might still be in New Zealand."
Organised gangs or career criminals could have been behind the theft, trading the paintings for drugs, guns, money, or even as leverage in the event they are arrested for another crime.
University of Canterbury criminologist Greg Newbold says they would be difficult to unload.
"It could be that someone has got these very expensive [Lindauer] paintings in storage as a useful bargaining tool," Newbold told the Herald earlier.
"Say you're involved in a criminal enterprise, importing methamphetamine say, having the Lindauer paintings would be a pretty good bargaining chip if you're picked up and charged."
Police have remained tight-lipped over their investigations.
In response to a series of questions this week by the Herald, a short response read: "Our investigation into this matter is ongoing and we are unable to comment any further at this time."
International Art Centre director Richard Thomson said he's had no updates lately.
"It was a lot more sophisticated than has been recorded," he said previously.
"We have very high security. Some things you just don't see coming.
"It's a dark day in New Zealand art history."
The dark web auction, posted by an anonymous seller going by the handle Diabolo, claimed the portrait was "100% genuine" and that the painting would be shipped in a wooden box within four days of the auction closing.
"Here you can bid on an TOP SECRET original Painting from Bohemian painter Gottfried Lindauer that was stolen in New Zealand, Auckland 2017," the listing said.
Marinello is "pretty much convinced" the listing was fraudulent.
"No new images were used and we have seen no indication that the person responsible for the posting had any access to the paintings," he said.
"No legitimate collector or dealer will touch these pictures. I'm afraid we are going to have to wait until someone tries to offer them for sale knowingly or unknowingly or law enforcement stumbles upon them during a search and seizure."
Jim Wheeler, chief executive of London-based ReSolve Cyber, says the dark web auction site has now been taken down.
"This can be due to successful law enforcement operations, technical difficulty (some criminals hack other criminals) or it has simply moved to another unlocated part of the darknet," Wheeler said.
