May has spoken by phone to European Commission President Jean-Claude Juncker twice in the past 24 hours.
The Irish airline said that it is putting plans in place to protect itself from a no-deal Brexit and ensure it will remain majority EU-owned and controlled. Citing officials in May's office, Sky News also reported she would travel to Strasbourg.
"Finally, the House of Commons is going to have to make a final judgment on what it wants in terms of Brexit", he said.
If her deal is defeated, May has pledged to give lawmakers a vote on Wednesday on leaving without a deal on March 29 and, if they reject that, then they will vote on Thursday on delaying Brexit.
According to Irish Foreign Minister Simon Coveney, May plans to travel to Strasbourg, France on Monday evening to finalize negotiations before bringing the divorce settlement to parliament.
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Talk of May stepping down as Prime Minister sooner rather than later is also growing, with her former policy adviser, Tory MP George Freeman, calling for "a new leader for a new generation" after Brexit.
"We've made an important offer again towards Great Britain and now of course it's up to Great Britain to react to these offers", Merkel said in Berlin.
May has promised Britain will leave the European Union whatever happens on March 29, but many MPs fear that a "no deal" exit would wreak economic havoc.
May's spokesman, James Slack, said "talks are ongoing" among lower-level negotiators and there was "a shared determination by both sides to find a solution".
"The deal that MPs voted on in January was not strong enough in making that clear - and legally binding changes were needed to set that right".
In a statement, the Commission said it had put forward proposals to try to reassure MPs the backstop "if used will apply temporarily".
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It could also include an addition to the political declaration too - a statement on what a future relationship between the United Kingdom and the European Union would look like - which will promise to work together for a free trade deal.
The third, another referendum on Brexit, has lost momentum in recent weeks, but that campaign could be reenergized if Brexit is postponed this week - not least because the minister in charge of Brexit has held talks with lawmakers in favor of a second referendum in the past few days.
Speaking in a joint press conference, Mr Juncker insisted that if the deal is not accepted by Parliament, then "Brexit may not happen at all".
This is far more likely, given that lawmakers rejected the deal in January by a historic margin of 230 votes.
Yvette Cooper, an opposition Labour Party lawmaker who has led efforts to hand parliament more control over Brexit, said parliament would try to take control of the exit process if May was unable to build a consensus. "Tuesday is about exposing the weakness of the prime minister".
The exact details of this vote are not yet known, including which way May will instruct her Conservative Party to vote.
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However, they have been playing their home games in the tournament at Wembley, because their new ground has yet to be completed. When you have the possibility to reach the quarter-finals, but everyone thinks the job is done, it's so risky .