Theresa May is due to make a statement on Brexit to MPs later, which will be followed by a debate on next steps.
MPs are then expected to vote on a series of alternatives to the prime minister’s Brexit deal.
Ministers were feeling “more positive” about being able to hold a third vote on the PM’s deal this week at a cabinet meeting this morning, sources said.
But Northern Ireland’s DUP has said its position has not changed and it will not be backing the deal.
DUP leader Arlene Foster told the prime minister the news in a telephone call after this morning’s cabinet meeting.
Mrs May’s EU withdrawal agreement has been overwhelmingly rejected in the Commons twice.
She has said she would only bring her deal back for a third Commons vote if there was “sufficient support” for it – and she spent the weekend trying to persuade Brexiteer Tories to get behind it.
But many are thought likely to take their lead from the DUP, which has led objections to the Irish backstop clause.
Meanwhile, the EU has said all its preparation for an “increasingly likely” no-deal scenario on 12 April has been completed.
Later, MPs are expected to back a plan to carve out parliamentary time for a series of so-called indicative votes on alternatives to Mrs May’s deal.
As many as six other options, in addition to Mrs May’s deal, could be put to votes to see which are most popular.
Conservative MP Sir Oliver Letwin told BBC Radio 4’s Today programme that once Mrs May knew what it would take to get a majority vote, it would help her find “a way forward in principle”.
But International Trade Secretary Liam Fox told the BBC that Parliament may want to look at a series of Brexit options, but they cannot be binding on the government.
“I’m answerable to my voters not to the House of Commons,” he said.
He told the Today programme there had to be an agreed deal by 11 April, otherwise the UK will have to take part in EU elections, which “would unleash a torrent of pent up frustration from voters”.