UK Prime Minister Theresa May is making a statement to MPs on the way forward on Brexit after her planned deal was rejected by MPs last week.
She hopes to win over Tory Brexiteer MPs and Northern Ireland's DUP, by resolving their concerns over the "backstop" plan for the Irish border.
Last week, Mrs May said she would focus on cross-party talks to get a Brexit deal accepted by Parliament.
Downing Street insisted that cross-party talks were continuing.
The backstop is the "insurance policy" in the withdrawal deal, intended to ensure that whatever else happens, there will be no return to a visible border between Northern Ireland and the Irish Republic after the UK leaves the EU.
Both the UK and the EU believe that bringing back border checks could put the peace process at risk. But a way of avoiding those checks has yet to win over MPs.
The DUP, which keeps Mrs May's minority government in power through a deal to support it in key votes, rejected her Brexit deal last Tuesday, but 24 hours later helped her see off a bid to oust her in a no confidence motion, saying it didn't want a change of government, just a change of policy.
Mrs May held a conference call with her cabinet on Sunday. It is understood she wants to show the EU that MPs could back a deal without a backstop, in the hope of encouraging Brussels to soften its position.
Meanwhile BBC political editor Laura Kuenssberg has suggested Mrs May may announce that fees will be waived for EU nationals who want to live in the UK after Brexit:
May expected to promise 'she will consider how we might meet our obligations to the people of Northern Ireland and Ireland in a way that can command the greatest possible support in the House, and then take these conclusions of these discussions back to the EU'— Laura Kuenssberg (@bbclaurak) January 21, 2019
May on her feet in Commons shortly - she 'll say more work to do on backstop, but hearing also she might scrap the fee for EU nationals who want to stay after Brexit, and promise select committees and other parties a bigger role in second phase of the negotiations— Laura Kuenssberg (@bbclaurak) January 21, 2019
Norman Smith, BBC assistant political editor, said anyone waiting for a Plan B would be "stuck at the bus stop for an awfully long time".
He said that reports over the weekend of the possibility of a bi-lateral agreement with the Irish Republic or a rewriting of the Good Friday Agreement had been "kiboshed" by both governments.
"It is back to the backstop and trying to find some sort of breakthrough," he added.
Mrs May's government agreed a withdrawal deal with the EU in November - covering topics such as the "divorce bill" and the Irish border - but it was rejected by MPs by a majority of 230 votes.
If Parliament doesn't approve a withdrawal agreement, the UK is due to leave the EU on 29 March without a deal or transition period.
What is happening on Monday?
The prime minister addresses the Commons on Monday afternoon, setting out how she intends to proceed with the Brexit withdrawal agreement.
She will also table a "neutral" motion, simply saying that the Commons has considered her statement, which will be debated and voted upon on 29 January.
This motion is expected to attract amendments from groups of backbenchers seeking more of a say in the process.
MPs are expected to table bills which could take a no-deal Brexit off the table, and potentially suspend Article 50 - which allows the UK to leave the EU.
Why does the Irish backstop matter?
Under Mrs May's deal, if there is not a trade deal or other agreement between the UK and the EU when the transition period ends, the backstop kicks in.
It would see Northern Ireland staying aligned to some rules of the EU single market.
It would also involve a temporary single custom territory - effectively keeping the whole of the UK in the EU customs union - unless both the EU and UK agree it is no longer necessary.
But this has been a huge issue for many Conservative MPs and the DUP, who have supported Theresa May's government since the 2017 election.
Removing or amending the backstop could provide Mrs May with enough backing from Brexiteer Tory MPs and the DUP to get an agreement passed.
How could MPs take control of Brexit?
Theresa May's government is engaged in a battle with MPs over who controls the Brexit process, after her deal with the EU was defeated by a record-breaking 230 votes last Tuesday.
MPs are trying to use various Parliamentary tactics to tell Mrs May what to do - or force through alternatives to her Brexit deal.
They can do this by tabling amendments - suggested changes - to a government motion, which is due to be voted on next Tuesday. Or by proposing new laws of their own.
One group of MPs, headed by Labour's Yvette Cooper, with backing from Remainer Conservative MPs, is planning to table a bill that would delay the UK's planned departure date from the EU if the government is not able to get its deal through by 26 February.
Private Members' Bills - laws proposed by MPs who are not in the government - can be passed but there's normally only very limited time to debate them. The government usually controls the agenda - what gets debated in Parliament.
Some MPs now want to suspend the normal rules to allow time to debate and vote on a bill that would rule out a no-deal Brexit.
That might not be enough though. If the bill will involve spending money it also needs a "money resolution". That has to be proposed by the government.
So MPs face another obstacle if they want to take control of the Brexit process.
What's the view from the EU?
European Commission Margaritis Schinas said: "Don't look for answers to Brussels … this is the moment for London to speak, not for us."
But Poland's Foreign Minister Jacek Czaputowicz has told the BBC that he has suggested time-limiting the Irish border backstop as a means of "unblocking" the negotiations.
He said he had discussed his proposals with Ireland's foreign minister Simon Coveney and the UK's Foreign Secretary Jeremy Hunt, but did not know whether it was "feasible".
German's foreign minister Heiko Mass said he had confidence in Mrs May but did not know if it was too late to get a deal.
Miroslav Lajcak, Slovakia's foreign minister, said reopening the Withdrawal Agreement was not feasible and there was no point in delaying the UK's planned departure date.
What is Labour's position?
Mrs May invited Jeremy Corbyn to cross-party talks on Brexit after she survived a vote of no confidence in her government last week.
But the leader of the opposition said he would only enter cross-party talks if the prime minister took the possibility of a no-deal Brexit off the table.
Mrs May said that was an "impossible condition".
Labour's position since Mrs May's withdrawal agreement was rejected by the Commons is to seek a general election - if that fails they would consider backing a second referendum.
Mr Corbyn has previously said Labour wants a customs union with the EU, tariff-free access to the single market and an EU-level of employment rights to be included in any Brexit agreement.
Shadow International Trade Secretary Barry Gardiner told BBC Leeds his party would back a motion in favour of another referendum.
But the Labour leadership's position is not thought to have changed, and it will be tabling an amendment next week on Labour's customs union plan.
A spokesperson for Mr Gardiner said: "'Barry is committed to Labour's policy of pushing for a general election as the best outcome.
"If the Conservatives block an election we will keep all options on the table, including campaigning for a public vote. Whipping arrangements will be decided in the normal way in due course."