The EU has offered the British government the right to unilaterally exit from the UK-wide parts of the Brexit backstop.
Michel Barnier, the EU’s chief Brexit negotiator, said on Friday this would stop the UK being “forced into customs union against its will”.
In a series of messages on Twitter, Barnier said the Brussels had proposed a “legally binding interpretation” of the Withdrawal Agreement.
But under the proposal, the Northern Ireland-only backstop would remain in place indefinitely if a future trade deal is not agreed.
Such an offer has already previously been rejected by Theresa May and pro-Brexit Tories.
It is also unlikely to convince the DUP, who have said it would be unacceptable as it would create a customs border between Northern Ireland and the rest of the UK.
MPs are expected to reject May’s deal when it’s put to a vote on Tuesday. If the Commons votes down her deal, the PM has pledged to give MPs a vote on accepting a no-deal Brexit, or on delaying Brexit.
In a warning ahead of next week’s Commons showdown, the prime minister acknowledged “no one knows” what will happen if her plan is defeated.
In a speech on Friday, May said both the democratic and economic cases for backing her deal are “clear”, and issued a plea to MPs: “Let’s get it done.”
She also said what the EU does over the next few days “will have a big impact on the outcome of the vote”.
“Next week, MPs in Westminster face a crucial choice: Whether to back the Brexit deal or to reject it,” she said.
“Back it and the UK will leave the European Union. Reject it and no-one knows what will happen.
“We may not leave the EU for many months, we may leave without the protections that the deal provides. We may never leave at all. Rejection of the deal would be a ‘moment of crisis’.”