EU chief negotiator, Michel Barnier, has claimed that the UK-EU Withdrawal agreement is "the best possible deal", including the controversial Irish backstop, in an interview with Irish broadcaster RTE.
However there were signs some Brexiteers could reluctantly back Mrs May's deal amid concerns a cross-party grouping of MPs are plotting to impose a "softer" Brexit - or derail it altogether.
Attempts to reach a compromise Brexit vision with Labour have not worked, and May is now reportedly trying to win over rebel MPs in the Tory party.
The plan B motion will be laid out on 21 January, while MPs are set to vote on it on 29 January.
Following the crushing defeat last week of her agreement with Brussels, the Prime Minister will make oral and written statements to the House explaining how she intends to proceed.
It is understood she wants to show the European Union that MPs could back a deal without a backstop, in the hope of encouraging Brussels to soften its position.
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Irish foreign minister Simon Coveney was adamant over the weekend the backstop - meant to ensure there is no hard border between Northern Ireland and the Republic - was an essential part of the Withdrawal Agreement.
With just weeks to go before Britain is due to leave the EU, Mrs May will return to Parliament on Monday to set out how she plans to try to break the Brexit deadlock after her deal was rejected by lawmakers last week.
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Cabinet sources have told Sky News that Mrs May made clear she was ditching efforts to seek a cross-party compromise, because the level of support expected from Labour MPs was not deemed strong enough to pass the Withdrawal Agreement and the subsequent Brexit legislation required before the United Kingdom leaves the EU.
"May's no-deal threat is empty and hugely expensive, wasting billions of pounds we should be spending on vital public services", he said.
May's spokesperson was previously cited by Reuters as saying that the prime minister was not taking a "no deal" Brexit option off the table after a request by Labour leader Jeremy Corbyn.