The government will also order its MPs to vote against a move which could delay Brexit by up to nine months.
Parliament will vote on proposals made by lawmakers including a delay to Brexit and going back to the European Union to demand changes to the Northern Irish backstop.
International Trade Secretary Liam Fox, however, insisted that backing the amendment would strengthen the Prime Minister's hand when it came to reopening negotiations on the backstop - meant to ensure there is no return of a hard border on the island of Ireland.
The prime minister's original Brexit proposals were thrashed by the parliament on January 15, with the government losing by record 230 votes.
The EU has repeatedly insisted it will not renegotiate the backstop arrangement, which is created to protect the border between Northern Ireland and the Republic of Ireland and prevent harming the Good Friday Agreement.
The backstop mechanism in the Withdrawal Agreement would keep the United Kingdom in a "single customs territory" with the EU.
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It is reportedly backed by members of both the Remain and Leave camps of the Conservative party.
Should the attempt to renegotiate the backstop fail, the second stage would see the PM ask the European Union to honour the agreed transition period.
Sir Ivan, the UK's former permanent representative to the European Union, refused to speculate on the outcome of the next House of Commons vote but insisted it was fuelled by a lack of understanding of the withdrawal agreement negotiated by the Prime Minister.
"What a cunning plan", one European Union official is said to have remarked sarcastically, while an European Union diplomat was reported to have said, "This is just nonsense", according to The Guardian.
Former Cabinet minister Nicky Morgan said discussions had been taking place for "some days" between herself, health minister Stephen Hammond, and Solicitor General Robert Buckland on one side and Mr Rees-Mogg and Steve Baker from the ERG on the other.
This would give both sides time to prepare for a departure on WTO terms at the end of 2021 - or to strike a new trading relationship.
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Speaking to BBC Radio 4's Today programme, Duncan Smith said today that the proposal was "the best hope we've got".
An EU official also confirmed to the Guardian that such a response could be expected. May has urged her party to vote for the Brady amendment.
Mrs May addressed a meeting of her backbench MPs on Monday night and numerous sources told the BBC's political correspondent Iain Watson that she would be backing what is known as the "Brady amendment" - a measure put forward by Sir Graham Brady, the chairman of the backbench 1922 committee of Conservative MPs. "We need to have a majority that doesn't just get agreement over hurdle of a meaningful vote by a narrow majority but we need to have a stable majority to ensure the ratification", she said. The party's leader, Jeremy Corbyn, will consider his next steps carefully, as polls show that his inconsistent stance on Brexit is costing him public support, especially among young people.
The Prime Minister's Brexit deal proved so unpopular the government fell to a historic defeat when parliament voted on it in December, losing by a record 232 votes.
But Ireland's Mr Coveney reiterated that the backstop was crucial in preventing a hard border and told the Press Association that "peace and the Good Friday Agreement are more important than Brexit". "We're not going to reopen the agreement". Lawmakers in her own party want her to demand a last-minute change to the withdrawal deal to remove the backstop, which they fear could end up trapping the United Kingdom in a permanent customs union with the EU.
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Kamala Harris (D-CA) and now 2020 presidential candidate made her case for stricter gun laws during her CNN townhall on Monday. But another billionaire businessman, former NY mayor Michael Bloomberg, strongly urged Schultz to halt his independent antics.