The law would also ensure businesses in Northern Ireland are able to disregard EU rules and regulations and remove the power of the European Court of Justice to rule on issues relating to the region, the paper said.
Importantly, the bill would override the protocol agreed by Prime Minister Boris Johnson in 2019 and mean the UK had breached its obligations under the Brexit agreement.
The Times said Ms Truss is understood to have concluded talks with the EU and has been told the proposed bill could lead to a trade war with the bloc.
It comes after The Sunday Telegraph said Ms Truss faces Cabinet opposition, particularly from Chancellor Rishi Sunak and Communities Secretary Michael Gove, to her plans to rip up the protocol.
UK-EU discussions on the Northern Ireland Protocol need to be intensified, the Irish premier has told Boris Johnson.
In a call on Tuesday morning, Taoiseach Micheal Martin spoke to the UK Prime Minister about the challenges facing Northern Ireland following the Assembly election.
He tweeted: “We both agreed on the need to see the NI Executive formed as soon as possible.
“On the Protocol, I stressed need to intensify EU and UK discussions, and to avoid any unilateral action.”
Sir Jeffrey Donaldson, meanwhile, has said that he will not lead the DUP back into powersharing until the issue is resolved, suggesting the prospects of any quick return of the devolved powersharing Executive at Stormont are diminishing.
MLAs returned to Parliament Buildings on Monday and party leaders were also holding separate meetings with Secretary of State Brandon Lewis.
Sinn Fein vice president Michelle O’Neill said that the DUP and British Government must accept and respect the democratic result of the Northern Ireland Assembly elections.
The Prime Minister has said he does not plan to be personally involved in the Northern Ireland talks, while Downing Street played down the reported Cabinet rift over the protocol.
Asked about the Government’s position on the protocol and whether there are divisions within Cabinet over proposals to unilaterally scrap it, Mr Johnson’s official spokesman said: “I wouldn’t say that at all.
“I think our preference has always been for a negotiated solution to fix the protocol and we have been clear that we will take further steps if solutions can’t be found.
“No decisions have yet been taken on the way forward. The Deputy Prime Minister made clear the situation, it’s very serious.”
He insisted the proposals put forward by the European Commission “don’t go anywhere near far enough to make the protocol sustainable”, adding: “We believe (they) would take us backwards from where we are today. So no decisions have been taken. But we do reserve the right to take action.”
That line echoed earlier comments on Monday by Tory MP Michelle Donelan, in which the universities minister said scrapping the protocol was “on the table as one of the options” in the wake of Sinn Fein’s success in the Stormont elections.