Theresa May is set to hold talks with Irish leader Leo Varadkar as she tries to break the deadlock over the Irish border backstop.
The prime minister is to fly to Dublin to resolve a dispute over the mechanism after spending Thursday in talks in Brussels.
The backstop – a customs plan to avoid a hard border between Ireland and Northern Ireland if a Brexit deal is not reached – remains the main stumbling block in Mrs May’s plan to take the UK out of the European Union.
Meanwhile, Attorney General Geoffrey Cox will meet with his Irish counterpart Seamus Woulfe.
He has been working within Whitehall to either provide a time limit on the backstop or give the UK way to ditch the backstop unilaterally if it needs to.
The plans have been met with scepticism in Dublin, which says the backstop cannot be time-limited if it is provide an insurance policy against the return of a hard border on the island of Ireland.
However, the prime minister has warned she needs legally-binding assurances that Britain will not be tied to EU rules indefinitely through the backstop.
Before their meeting over dinner, the Taoiseach will meet with the main parties in Northern Ireland in Belfast on Friday.
Elsewhere, ministers are looking with interest at a letter from Labour leader Jeremy Corbyn setting out the terms by which his party would back a deal in the Commons.
Labour Remainers have voiced their anger over fears the plan would kill their hopes of their party supporting a second referendum.
However, Downing Street sources said there were still very considerable points of difference with Labour vision of staying in the customs union after Brexit.
Mrs May may be hoping the threat of MPs backing a softer Norway-style deal if there is no agreement on the prime minister’s proposal will force some Tory Brexiteers to back her plan.
A Norway-style deal would see the UK becoming a member of the European Economic Area and the European Free Trade Association – gaining access to the single market and limited EU trade barriers.
During Brussels talks on Thursday, Mrs May won commitment from Jean-Claude Juncker, the president of the European Commission, that their teams would carry on talking to find a solution which will be backed in the Commons.
They are to meet once more to assess the situation before the end of the month.
However, the EU is adamant it will not re-open the Withdrawal Agreement – the agreement between the government and the EU on the terms of the UK’s departure – as the European Council president, Donald Tusk, said there was no breakthrough in sight.
But German Chancellor Angela Merkel was more encouraging, saying a deal was possible without re-opening the Withdrawal Agreement.