But at least 12 British Ministers, including those responsible for "brakcet" Dominic Raab, are not going to change its position and require Mei to call the exact timing of actions, the so-called interim solution on the Irish border.
However, Leo Varadkar, the Irish prime minister, said that Dublin was open to the idea of a "review mechanism" for the backstop that had been put forward by Mrs May in a telephone call. This would negate the need for checks at the Border.
British media reports that Mrs May had already concluded a "secret deal", were dismissed by negotiators.
"These ideas are not backstops at all + don't deliver on previous United Kingdom commitments".
'The Irish stance is still the same and clear to say that an emergency time-bound plan or one that could be unilaterally completed by the United Kingdom will never be agreed upon by the country or the European Union, ' said Irish Foreign Minister Simon Coveney on Twitter.
May is under intense pressure from several members of her cabinet to secure a mechanism by which any backstop agreements can be time limited and able to be terminated by the UK.
The publication states that the arrangement will will also include an "exit clause" that will aim at convincing Brexiteers that remaining in the customs union is only temporary.
The Irish border has proved the biggest obstacle to a deal, with both sides vowing not to create a hard border between Ireland and Northern Ireland for fear of destabilising the peace accord that ended decades of deadly sectarian violence.
The DUP's Donaldson, whose party has repeatedly criticized Dublin's approach, said a no-deal Brexit would have serious consequences for Ireland's economy and he "can't understand why Irish Government seems so intent on this course". "The small print is that Ireland is f*****".
It comes amid reports of an imminent deal - which Downing Street has described as "speculation". The government has previously said the withdrawal agreement is 95 percent complete and that there's also been progress in talks on the future relationship.
"Looks like we're heading for no deal", Jeffrey Donaldson, one of 10 Democratic Unionist Party (DUP) lawmakers whose support May now needs to get any deal passed in the British parliament, said on Twitter.
Mr Howlin said he was concerned Ireland had been "boxed into a corner where the backstop issue is the one remaining issue" and faced incredible pressure as a result.
"I certainly hope we are".
He said there was a "rapidly ticking clock" but that minds were now being focused with a view to concluding a deal and he welcomed that.
British housing minister James Brokenshire said on Sunday there was still an issue around Northern Ireland in the Brexit talks, referring to a yet-to-be finalised "backstop" arrangement which would prevent a hard border between Northern Ireland and European Union member Ireland if no better solution can be found.
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