Theresa May has said she will talk to the EU later about reopening negotiations on how the UK leaves the bloc on 29 March.
She is expected to have phone calls with key EU leaders throughout the day ahead of a series of Commons votes over the future direction of Brexit.
The EU has ruled out making changes to the legal text agreed with the UK PM.
But Mrs May has told her cabinet she will seek legally binding changes to the controversial Irish backstop.
Senior Brexiteer rebels – who voted down her deal last month – have indicated they would be willing to back her deal if she gets legal changes to the backstop.
The backstop is the insurance policy in Mrs May’s plan to prevent checks on good and people returning to the border between Northern Ireland and Ireland, which some MPs fear could leave the UK tied to the EU’s rules indefinitely.
MPs have put forward a string of amendments to modify the prime minister’s Brexit plan after it was voted down by an historic margin on 15 January.
Speaker of the House, John Bercow, will decide which of the amendments can be debated at around 13:45 GMT and Mrs May will then open the debate.
A vote on the amendments is then expected at around 19:00 to see which ones have the support of MPs.
Conservative MPs have been instructed by the government to vote for an amendment calling for “alternative arrangements” to the backstop, proposed by senior backbencher Graham Brady – if it gets chosen by Mr Bercow.
International Trade Secretary Liam Fox has said the “Brady” amendment would give the PM a “strong mandate” to return to Brussels, adding: “If you compromise with us on this one issue, on the backstop, we would be able to a get an agreement – an agreement that is almost there.”
Former foreign secretary and leading Brexiteer Boris Johnson gave a boost to the plan, saying he “gladly” vote for the amendment, if Mrs May confirmed she would re-open negotiations with Brussels.
But it is not the only amendment on the table.
The Labour party and a number of Remain-backing MPs are supporting an amendment by Labour MP Yvette Cooper that would create a bill enabling Article 50 – the mechanism by which the UK leaves the EU – to be delayed by up to nine months if the government does not have a plan agreed in Parliament by the end of February.
Labour said it was supporting the amendment because the bill it would create could “give MPs a temporary window to agree a deal that can bring the country together”.
But they would “aim to amend the Cooper bill to shorten the possible Article 50 extension”.
Some members of Mrs May’s cabinet, including Work and Pensions Secretary Amber Rudd, had called for a free vote on Tuesday’s amendments to allow them to back Ms Cooper’s proposal, but the government is whipping against it.
Mrs May is said to have tried to reassure her cabinet this will not be their last chance to vote on the next steps of Brexit, promising to return to the Commons “as soon as possible” with a revised deal and offering a second “meaningful vote” on her proposals.
If no new deal is reached by 13 February, the PM will make a statement to Parliament that day and table an amendable motion for debate the following day, re-opening discussions on how to move forward with Brexit.
Will MPs find agreement in their plans?
The government’s ambition is so low – or its hurdles so high – that what No 10 seeks to do on Tuesday is not to win (326 is a majority in the House of Commons), but to reduce the scale of resistance to their central policy that, in the words of another cabinet minister, only the “hardliners oppose”, so that Theresa May can get the rebels down to a “few dozen”, so then they can crack on.
Separately, Conservative MPs on both sides of the Brexit argument have been planning for a no-deal scenario.
Former Remainers, including ex-Education Secretary Nicky Morgan and government ministers Stephen Hammond and Rob Buckland, have been working with Brexiteers Jacob Rees-Mogg and Steve Baker on the plan – in talks co-ordinated by Conservative MP Kit Malthouse.
According to a leaked document, the proposal drawn up by the rival factions would extend the transition period – during which the UK would continue to follow EU rules and pay into its budget – from the end of 2020 to December 2021, to allow more time to reach a free trade deal.
EU citizens rights would be guaranteed during this time, there would be no customs checks on the Irish border and the UK would pay the £39bn so-called “divorce deal”.
The Democratic Unionist Party (DUP) – which props up Mrs May’s government – has endorsed the “Malthouse” proposals.
DUP leader Arlene Foster said the plan could “unify a number of strands in the Brexit debate” and was a “feasible alternative to the backstop proposed by the European Union”.
But the EU was “standing tough” on its position of no renegotiation and they were “mesmerised” with what was happening in Parliament, BBC Europe editor Katya Adler said.
Senior EU representatives have repeatedly ruled out reopening negotiations with the UK over Brexit, and have insisted the backstop must be included in any deal.
And Ireland’s European Affairs Minister, Helen McEntee, said: “There can be no change to the backstop. It was negotiated over 18 months with the UK and by the UK.”
The European Research Group, led by Eurosceptic Mr Rees-Mogg, had initially said the group would not back the amendment.
But Mr Rees-Mogg told the BBC on Tuesday that if the Brady amendment had government support and if it meant reopening the withdrawal agreement – the part of Mrs May’s deal that lays out how the UK will leave the EU – it would be “very different” from a backbench plan.
“Let’s see what the prime minister says at the despatch box today and what the Brady amendment really means,” he said.
Will Brussels budge on the Irish backstop?
By Katya Adler, Europe editor
The EU certainly never intended to budge on the backstop – painfully negotiated with the UK over 18 months and signed off last November by Mrs May and her cabinet.
But Europe’s leaders didn’t imagine the UK would still be in such flux over Brexit so very close to B-day on 29 March.