Michel Barnier, the European Unions (EU) chief Brexit negotiator, has told member states that the British government has till Friday evening to agree on a potential deal or else negotiations will not move on to the next stage.
Barnier informed EU ambassadors that Downing Street had told him a potential solution was being worked out that could possibly satisfy both Northern Ireland's Democratic Unionist Party (DUP) and Ireland, but that it had yet to be signed off by any of those involved, the Guardian reported on Thursday.
Another meeting of diplomats of the 27 member states has been scheduled for Friday evening.
If the UK fails to agree a joint position with the European commission by Friday, the member states informed Barnier that they would not have time to take it back to their capitals for scrutiny ahead of next week's critical European council meeting.
In that scenario, the leaders would once again rule that insufficient progress had been made on the opening issues of citizens' rights, the financial settlement and the Irish border for talks on trade and a transition period to start.
A failure to move talks on in December would mean that the terms of a transition period could potentially only be discussed after the next European council summit of leaders in March 2018, by which time key businesses in the UK will have had to make decisions over their location and investments in the country, the Guardian reported.
It is possible that the leaders would call an emergency summit in January or February 2018 to agree to move talks on and discuss the terms of a transition period.
The UK is set to exit the EU by March 2019.