Brexit: Nothing off table for Theresa May ahead of key vote
"Nothing is off the table" when it comes to reassuring MPs over the Northern Ireland backstop, Downing Street sources say.
This could include reopening the EU withdrawal agreement, even though that comes with risk, the sources say.
Theresa May is understood to be pushing the EU for flexibility on the backstop.
This is the clause in the prime minister's EU withdrawal agreement that is meant to prevent the return of border checks in Northern Ireland.
It would see the UK aligned with EU customs rules until a future trade deal is agreed that does not include a physical border between the EU and the UK on the island of Ireland.
The backstop is meant to be a temporary measure but the UK can't leave it without the EU's say-so, under the terms of the withdrawal agreement.
Many MPs fear this will mean the UK will end up indefinitely tied to the EU with no say over its rules - and that is why they are planning to vote against the withdrawal agreement on Tuesday.
Those campaigning for another EU referendum have, meanwhile, been given a boost by the European Court of Justice (ECJ), which has ruled that the UK can cancel Brexit without the permission of the other 27 EU members.
Former foreign secretary Dame Margaret Beckett, who is campaigning for another referendum, said: "This is confirmation that it is still up to us to decide whether we want to keep the existing deal we've got in the EU rather than accept a bad deal negotiated by the government."
But Environment Secretary Michael Gove said the ruling does not alter the government's intention to leave the EU in March 2019.
He told BBC Radio 4's Today programme: "We voted very clearly - 17.4 million people sent a clear message that we wanted to leave the European Union and that means also leaving the jurisdiction of the European Court of Justice.
"So, this case is all very well but it doesn't alter either the referendum vote or the clear intention of the government to make sure that we leave on 29 March."
He rejected newspaper reports that Tuesday's Commons vote will be cancelled to prevent the prime minister suffering a defeat of historic proportions that could end her premiership.
Mrs May has previously insisted there can be no deal with the EU without the backstop - and it would be impossible to change the terms of the withdrawal agreement.
She has repeatedly warned her own MPs that a rejection of her deal could lead to a general election - or possibly "no Brexit" at all.
That has so far failed to convince dozens of Tory MPs who are planning to join Labour, the Liberal Democrats, the DUP and the SNP in voting against it.
So, in a change of tone, Downing Street is now saying the withdrawal agreement could be tweaked to reflect concerns about the backstop.
By BBC Political Editor Laura Kuenssberg
On the face of it, it's pretty extraordinary to imagine that the UK government could be genuinely asking to reopen an agreement that took 18 months to put together, has already been through the grinder on multiple occasions and was only concluded a fortnight ago.
But since the ink dried, it has become clear that the chance of getting the deal through Parliament is very small. One minister said: "It's only a deal if it's ratified." Perhaps for wavering MPs, even the sign of the PM continuing to push for more will make a difference.
Mr Gove said the prime minister was "seeking to improve" the agreement but there were "risks" involved.
"If we do attempt a fundamental reopening or renegotiation of the withdrawal agreement, European Union countries, who recognise just how uncomfortable the backstop is for them, may change the withdrawal agreement in a way that may not necessarily be to our advantage," he said.
He said it was "extremely unlikely" that he would mount a Tory leadership challenge if Theresa May stood down or was forced out after losing Tuesday's vote.
On Sunday evening, Mrs May spoke on the phone to Irish Prime Minister Leo Varadkar, whose support could be vital if she were to negotiate further with the EU.
She also spoke to the European Council President Donald Tusk, who tweeted it would be "an important week for the fate of Brexit".
Boris Johnson said Mrs May could stay on if she lost Tuesday's vote - but must renegotiate the deal with Brussels.
Mr Johnson, who quit the cabinet over Mrs May's Brexit strategy, told the BBC he did not want a "no-deal" Brexit or another referendum, but it was not right to say there were no alternatives.
He said the Northern Ireland "backstop" put the UK in a "diabolical negotiating position".
MPs could give Mrs May "a powerful mandate to change that backstop" by voting it down on Tuesday, he said.
Former Cabinet minister and Leave campaigner Theresa Villiers has said that the UK could cope with a no-deal scenario if "preparation is stepped up" and the EU co-operated.
Meanwhile, Lib Dem leader Sir Vince Cable believes Brexit may not happen at all.
"Increasingly I doubt it," he said when asked about it becoming a reality, adding it was "more likely that it won't happen".
He added there could be a "hell of a backlash" if Mrs May's "economically damaging" Brexit were to be imposed without another referendum.