The Stormont Assembly could be recalled to approve emergency measures dealing with the overspend on Northern Ireland's botched green energy scheme, the DUP claimed.
But a senior Sinn Fein minister said he was "bemused" amid reports a proposal had been drawn up to address the potential £490 million taxpayers' bill.
The Department for the Economy, under the DUP's Simon Hamilton, plans to seek coalition partners Sinn Fein's backing for the move.
Mr Hamilton said: "I hope we would be able to get from my department a paper to the Executive in the next number of days for approval.
"It would be my hope then that we might be able to bring that to the Assembly as early as next week."
Sinn Fein Finance Minister Mairtin O Muilleoir said the DUP had not contacted him.
He added: "I am bemused at the trailing in the media of a DUP plan to resolve the Renewable Heat Incentive (RHI) debacle when not one scrap of paper detailing this 'plan' has been received by the Department of Finance.
"I am alert to the dangers of allowing the person who was the architect of the RHI scheme - the DUP leader - to come up with a solution to this debacle. That is why I will ensure my officials rigorously test any plan which comes from the DUP.
"I will be guided solely by what is in the interest of the public purse.
"The DUP are in a hole and should stop digging."
First Minister Arlene Foster has claimed measures being drawn up by Mr Hamilton could clear Stormont's bill.
"There will be no overspend," she said.
Mr O Muilleoir said: "Every plan produced by the Department of the Economy on this issue has been flawed."
Mrs Foster has accused political rivals and social media trolls of misogynistic attacks.
She has been under intense pressure for weeks over her handling of the RHI scandal.
All rival parties at Stormont have demanded she stand aside while her role in the affair is investigated. Mrs Foster oversaw the inception of the RHI scheme during her time as economy minister.
Senior members of Sinn Fein have warned they will exercise their power to collapse the powersharing Executive if Mrs Foster does not temporarily stand down to facilitate a probe.
If the republican party follows through with that threat Northern Ireland will be facing a snap Assembly election, less than a year after the last one.
Again making clear she would not be stepping down, Mrs Foster has said the head of Northern Ireland's Civil Service and its Attorney General had drawn up terms of reference for an independent probe into the RHI.
However, Sinn Fein, whose sign-off would be required, rejected the proposed terms of reference as "insufficient" and insisted any probe must be time-limited and have powers to compel witnesses and subpoena evidence.
The state-funded RHI was supposed to offer a proportion of the cost businesses had to pay to run eco-friendly boilers, but the subsidy tariffs were set too high, and without a cap, so it ended up paying out significantly more than the price of fuel.
This enabled applicants to "burn to earn" - getting free heat and making a profit as they did it.
Claims of widespread abuse include a farmer allegedly set to pocket around £1 million in the next two decades for heating an empty shed.
It was originally envisaged that the Treasury would foot the bill for the RHI, but the costs spiralled well beyond London's financial commitment.
The total RHI spend in Northern Ireland is estimated at £1,150 million over the next 20 years.
The Treasury is set to cover £660 million of that, with Stormont landed with the remaining £490 million.