The EU's chief Brexit negotiator Michel Barnier on Friday proposed that Britain could leave the bloc's customs union after the divorce though the offer would not include Northern Ireland which will most probably anger London.
The last minute-bid by Barnier comes just days before British Parliament is due to vote on a withdrawal deal agreed between the two sides, in which the fate of the Irish border is seen as a key issue.
The EU commits to give UK the option to exit the single customs territory unilaterally, Barnier said on Twitter after a meeting with the ambassadors of the remaining 27 EU states.
However, the other elements of the backstop must be maintained to avoid a hard border, said Barnier, in reference to alignment between Northern Ireland and the EU-member republic.
Both the EU and Great Britain want to prevent a hard border that would bring controls between the British province of Northern Ireland and EU-member Ireland after the Brexit.
Without a solution in a future arrangement, the current deal agrees to keep the UK in a customs union with the EU until a better answer can be found.
But supporters of Brexit fear that Britain would then be trapped permanently in the EU, and have refused to back the deal.
The counter-offer will almost certainly be refused or ignored by the government of Prime Minister Theresa May, which depends on unionist MPs from Northern Ireland for its majority.
Putting a post-Brexit border in the Irish Sea is a strong red line that May's government has refused to concede.
Barnier's proposal aims to counter arguments from the British who say they want to trap the UK in a customs union, a European diplomat commented.
But it risks making Theresa May very angry, he added, because it goes back to an earlier version of the backstop, limited to Northern Ireland, which May insisted the EU abandon.
The British parliament is set to vote Tuesday on May's existing deal with Brussels after rejecting it by a historic margin in January.
The last-gasp negotiations between UK and EU envoys ended in acrimony on Wednesday and May still lacks the assurances she has been after to get her deal approved by MPs.