The Labor government foreshadowed the about-face at a briefing with big resources companies and Indigenous groups on Friday, The West Australian reported on Saturday.
An announcement is expected "within days", it added.
The new Aboriginal Cultural Heritage Act laws came into effect on July 1, after Roger Cook's Labor government resisted calls from pastoralists and the opposition to delay their introduction.
WA's previous laws dated back to the 1970s and notably allowed the state's Aboriginal affairs minister to grant land users permission to disturb cultural heritage sites.
Rio Tinto had ministerial approval in 2020 when it blew up the 46,000-year-old Juukan Gorge rock shelters, sparking global condemnation and devastating traditional owners.
The new system abolished the Section 18 approvals process and placed an emphasis on agreements between land users and traditional owners.
But there were deep concerns about the compliance requirements, some of which were only been made clear days before the laws came into effect.
More than 25 new local Aboriginal cultural heritage services were also being set up to manage sites within particular regions.
The government had flagged a "light touch" approach in the first 12 months to ensure stakeholders understood their obligations.
However the laws, which were proposed and established under ex-premier Mark McGowan, have proven controversial for Mr Cook, who has been bedding down his leadership since taking over in June.
Critics argued they were too complex and landowners feared their activities would be impacted.
Government agencies also expressed confusion about their requirements under the legislation.
Landowners concerned about the new laws were planning to gather on Tuesday at state parliament to call for changes to protect freehold property rights.
Opposition Leader Shane Love is due to hold a press conference in Perth later on Saturday.
WA Liberal senator Michaelia Cash said if the report is correct, it will be a humiliating backdown for the Cook government.
"Premier Cook should have listened much earlier and saved thousands of Western Australians, particularly farmers, the anguish and worry of the past few months," she said in a statement on Saturday.
"The chaos that was caused in Western Australia is an indication of what could happen if a voice to parliament is enshrined in our constitution," she added, referring to the national referendum on the voice due later this year.
Nationals Leader David Littleproud welcomed the expected scrapping of the changes, and called on Prime Minister Anthony Albanese to rule out federal Aboriginal heritage reforms that would replace the WA laws.
The WA laws were an overreach "requiring cultural surveys for even digging a hole", he said.
"Australian farmers have a strong record of protecting cultural sites and want to do the right thing," Mr Littleproud said.
"Labor must now explain how the federal reforms will work and rule out forcing property owners to undergo expensive mandatory cultural surveys and undermining private property rights."
