MPs have already voted against a "no deal" Brexit but this remains the default position unless they agree an alternative.
Parliament may take a series of votes this week to determine what proposals, if any, could command majority support.
This has been proposed by a cross-party group of lawmakers, led by Oliver Letwin, a member of May's Conservative Party.
Opposition leader Jeremy Corbyn raised the prospect of putting any proposal supported by lawmakers back to the people.
Prime Minister May has said she is completely opposed to the idea of revoking Article 50. Nothing the prime minister has offered so far would dampen the DUP's objections, the person said, noting that there was no further effort by the government over the weekend to persuade the party to back it. Some reports said ministers had "war-gamed" a national election. There are others calling for the government to provide time for indicative votes rather than ceding control of that process to Parliament, requesting a second referendum on Brexit, and suggesting lengthier delays to Brexit than the one now on offer.
The announcement was hailed as a way of preventing the United Kingdom crashing out without a deal on Friday, but with the government struggling to rally MPs behind the deal for a third time, and increasing pressure on the Prime Minister to step down, from sections of the Conservative Party, the European Union outlined details of its plans of what would happen were the United Kingdom to crash out of the European Union on April 12.
Lawmakers in a vote on Monday are likely to wrest more control of Brexit from May after twice rejecting the deal she agreed with Brussels.
Prime Minister, atleast till last week, was able to hold her Conservative party MP's together somehow, which broke away last week following deep frustrations in her Brexit deal and a increasingly hurry and hasty procedure to leave European Union.
A notice on Parliament's petitions site. Screenshot Katie Collins
Prime Minister Theresa should quit her post whatever happens, rank-and-file Brexiteer Nigel Evans told BBC Radio on Monday.
"What I was finding from real voters was people spontaneously saying: "I don't understand how Theresa May puts up with the pressure, she is a great public servant, her resilience is amazing", Dr Fox told Today.
"I'm not sure there's a majority in parliament in support of a second referendum", he said.
The first will see the Brexit deadline extended to May 22 if the British House of Commons approves Prime Minister Theresa May's withdrawal agreement next week. He was among those who participated in the Sunday talks with May.
"Options are narrowing and narrowing and narrowing", he said, predicting sterling would drop to as low as $1.20 with a no-deal Brexit and rise to at least $1.35-$1.40 if May's deal was passed.
"It is time for the PM to channel the spirit of Moses in Exodus, and say to Pharaoh in Brussels - LET MY PEOPLE GO".
Mrs May said: "It was never my intention that what I said should have the sort of impact that she is talking about, and I regret if it did have that impact because the point was a very simple one that I was trying to make, which is that we stand at a moment of decision for this House".