The government made concessions in talks with miners on the headline 40 percent tax rate, the Sydney Morning Herald said, quoting sources with knowledge of the talks.
The paper said the new trigger point for the tax would be around 12 percent of a return on capital.
That would be an increase from an initial proposal for about 5 percent, a rate based on the 10-year Australian government bond yield, the paper said on its website.
The tax deal would also give miners a break on retrospective projects, enabling them to roll lucrative iron ore operations in the Pilbara region in Western Australia and coal mines on the east coast, into the new tax regime at market value. This would be another key win for miners.
The Australian newspaper also reported an agreement had been reached and said it would be officially announced on Friday.
A government advisory said Gillard would hold a news conference in Canberra on Friday at 0830 a.m. (2230 GMT). The government and global miners Rio Tinto, BHP Billiton and Xstrata Plc, were locked in a second day of talks on Thursday over the tax.
None of the parties in the talks commented on the report.
But the chief of Australia's Atlas Iron told Reuters he understood "significant progress" had been made in the talks.
Under the original tax proposal, which was bitterly fought by miners, the big three miners would have shouldered around 80 percent of the tax.
"It's understood that BHP Billiton, Rio Tinto and Xstrata have agreed with the government now on the key elements of a new resources tax structure...," the Herald report said, citing sources close to talks between the government and miners.
"It was unclear at midday, east coast time, what deal had been struck on the headline rate, but the government is believed to have also given ground on this point," said the Herald, in a report written by a senior business columnist.
But any compromise should have input from the entire mining sector, iron ore producer Fortescue Metals Group said.
MARKETS RISE ON REPORT
The Australian dollar rose around a third of a cent after the report was issued.
Mining shares, in negative territory all week on lower metals prices, also jumped on the news with the metals and mining index up around 1 percent to erase much of the day's losses.
If the deal was confirmed it would leave the way open for new Prime Minister Gillard, appointed last Thursday, to call an election, possibly for August, to capitalize on her honeymoon rise in support and success in solving a bitter row with miners.
Whatever deal is reached between the government and miners, the fate of the tax still rests with the next parliament, with opposition parties vowing to reject it and key Green senators opposed to any watering down of the tax.
"We will rescind this tax in government, and we'll oppose it in opposition," opposition resources spokesman Ian Macfarlane told local media.
Rio Tinto chief executive Sam Walsh said on Wednesday that if a deal was reached, miners wanted an "assurance that it will carry through post the election if the government is re-elected."
Greens party leader Senator Bob Brown said on Thursday any tax agreement could not come with such guarantees.
"The mining tax legislation will come before the parliament after the election and there it will be properly scrutinized and most likely changed for the better," Brown told reporters.
The government had expected the tax to raise $12 billion ($10 billion) over the two years to July 2014, and had earmarked the money for infrastructure spending and to fund a cut in the company tax rate from 30 percent to 28 percent by mid-2014.
Treasurer Wayne Swan has repeatedly said any cut in revenue from the mining tax would not impact the government's forecast A$1 billion budget surplus in the year to June 30, 2013.
Any shortfall would likely come out of planned infrastructure spending or could prompt a delay or rethink on company tax cuts and plans to increase employer-funded pension benefits.
A mining tax agreement would remove uncertainty in the market and any watering down of the tax proposal is considered positive for investments and hence the Aussie dollar, say traders.
The proposed mining tax threatens more than $20 billion in investment, according to mining companies, but no major project has yet been scrapped and several have actually been advanced since the tax was unveiled on May 2.
The Herald said the new tax agreement was aimed at producing a simpler resource tax regime. Lower value resources including sand, gravel and limestone and nickel mining and processing, were expected to be excluded from the new resource tax, it said.
