Traditional owners, who have a deep connection to the land in the Hamersley Ranges, want it cleaned up.
Mr Wyatt says it is virtually impossible the area will ever be safe for human habitation, but it might be possible to remediate certain places of high cultural significance to the Banjima people and stop the contamination spreading into waterways or on the wind.
"Regardless of what I do, laws I pass, fences I put up, the Banjima people will still go onto that country," he told AAP.
It will be some time before the state government finalises its plan for Wittenoom, but companies that made money out of it should contribute to any clean-up costs, Mr Wyatt said.
"I suspect, as is often the case when these sorts of industrial disasters happen, it's usually the broader taxpayer that's left with the bill as companies appear very reluctant to pick up the obligations that they should meet on a moral as opposed to a legal basis."
A spokesman for Mr Hancock's daughter Gina Rinehart, who is Australia's richest person with an estimated net worth of about $15 billion, said it was little known that Hancock Prospecting and Wright Prospecting were not part of the large CSR operation that produced the tailings.
The three companies were involved in a smaller initial mine that closed when the bigger operation commenced, he said.
Ms Rinehart didn't inherit anything from her father's estate, which was bankrupt when he died in 1992, the spokesman said.
CSR did not respond to calls for comment.
KEY FACTS ABOUT WITTENOOM:
* About 20,000 people lived at Wittenoom at its peak
* More than 2000 died from asbestos-related diseases
* Three landowners have refused to move from the town, which was de-gazetted in 2007
* The state government is moving to oust them by compulsorily acquiring their properties
* Tourists still visit despite warning signs
* The state government plans to demolish the remaining houses, remove roads and erect more warning signs.