The British government is drawing up new proposals for a "review mechanism" in the Brexit withdrawal agreement, to allow the UK to escape any backstop arrangement if talks on a trade deal break down.
British Prime Minister Theresa May is thought to regard the idea as a means of allaying the concerns of Conservative and DUP MPs that Britain could be permanently trapped in a customs union with the EU as part of arrangements to avoid a hard border in Ireland.
Sources close to talks said London regarded it as a "big step" that the European Union side now appears ready to contemplate a means for bringing the backstop to an end short of a broader trade treaty.
Cabinet met for around three hours without reaching agreement on a final offer to present to Brussels.
But Mrs May raised the prospect of a possible second meeting within a week, as she assured senior ministers that Cabinet would gather again at an "appropriate moment" before a deal.
The Prime Minister said that she wanted to reach a withdrawal agreement as soon as possible, but "not at any cost".
Any agreement will be dependent on an "acceptable" framework for future relations in areas like trade and security, expected to be covered in a separate political declaration, she said.
It is understood that Attorney General Geoffrey Cox briefed cabinet on a range of options for the review mechanism, believed to include the possibility of an independent body ruling on whether talks had failed.
Taoiseach Leo Varadkar was accused in the Dáil of committing a "cock-up" when he told Mrs May yesterday he was ready to consider a mechanism, so long as it did not give the UK unilateral powers to quit.
He denied making a concession to UK demands for any backstop to be temporary, saying: "There can be no expiry date and there can be no unilateral exit clause, and if it were to be either of those things, the backstop would not be worth the paper it was written on.
"I'm open to creative solutions and creative language, but we will not resile from our fundamental resolution, the backstop cannot have a time limit or an exit clause."
Mrs May's official spokesman declined to be drawn on a timescale for agreement with the EU.
No additional cabinet meeting has yet been scheduled ahead of the regular weekly gathering next Tuesday, he told reporters, adding: "Don't be under any illusion, there remains a significant amount of work to do."
Hopes of a special Brexit summit to finalise the withdrawal agreement in November appear to be receding.
A gathering of EU leaders in Brussels on the previously mooted date of 17 November is now thought to have been ruled out, while a special summit later in the month would be dependent on EU negotiator Michel Barnier declaring that "decisive progress" has been made in talks.
Mr Barnier himself said a breakthrough on the Irish border issue was not close.
"For now, we are still negotiating and I am not, as I am speaking to you this morning, able to tell you that we are close to reaching an agreement," he told Belgian broadcaster RTBF.
"There is still a real point of divergence on the way of guaranteeing peace in Ireland, that there are no borders in Ireland, while protecting the integrity of the single market."
