The aim of the deal is to overcome a major roadblock in the negotiations: the now infamous Irish backstop.
"Tomorrow the House of Commons will debate the improved deal that these legal changes have created".
If Parliament throws out May's deal again, lawmakers will vote on whether to leave the European Union without an agreement - an idea likely to be rejected - or to ask the European Union to delay Brexit beyond the scheduled March 29 departure date.
In particular, the lawmakers advised the prime minister in phone conversations that she should delay the vote and put forward a motion describing a divorce agreement that would finally heal divisions over the issue within May's own party, the media outlet said.
"There is a widely held view that the United Kingdom has not been negotiating in good faith over the last few days", he said, adding that at least one diplomat had mentioned planning for a "post-Theresa May government".
In a significant intervention at the weekend, Steve Baker, a leading Conservative Brexiteer, and Nigel Dodds of the DUP - the Northern Irish party on whose support May relies for a working majority in parliament - wrote a joint article for the Sunday Telegraph newspaper insisting that it was "inevitable" that the deal would be voted down on Tuesday because it was unchanged.
'I think it would be very hard for the prime minister to stay in office for very much longer, ' she told BBC Radio 4's The World This Weekend.
"We will essentially be voting on exactly the same Withdrawal Agreement that we voted on last time and in very simple terms: if you ask the same question you are likely to get pretty much the same answer", said Mark Francois, a pro-Brexit lawmaker in May's Conservative Party.
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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 EU is preparing for a delay to Brexit of at least a year, senior officials and diplomats have said.
Tory Brexiteers said rejection of the Withdrawal Agreement was "inevitable" unless the prime minister could secure significant changes to the Northern Ireland backstop.
In the face of a cabinet revolt, she promised that if her deal is defeated again then MPs will vote on "no deal" on Wednesday and then on Thursday, on delaying Brexit. Parliament must approve the deal before it can be ratified.
The airline is to put plans in place to protect themselves from a no-deal and wants to ensure they will remain a majority European Union controlled and owned airline. They look set to defeat it a second time, with the United Kingdom due to leave the bloc on March 29.
The apparent breakthrough during talks between May and Juncker in Strasbourg came ahead of a vote on May's Brexit deal in the British Parliament.
For all of the prime minister's weaknesses as a politician - her repetition of talking points has earned her the nickname "the Maybot" - she has proved remarkably durable.
May has already survived a leadership challenge from within the Conservative Party, which means there can not be another one before December.
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It also showed a stone-faced Bolton during a meeting in Hanoi, while Trump and other U.S. participants were all smiles.