Northern Secretary James Brokenshire will travel to Dublin tomorrow for talks with Minister for Foreign Affairs Simon Coveney.
It will be their first meeting since the British government published two papers last week on its Brexit strategy.
They are also likely to explore their options on resuming talks with the five main Stormont parties about the restoration of power-sharing, which collapsed in January, following a row between the two main parties, the DUP and Sinn Féin.
Sinn Féin has written to both governments, suggesting that negotiations should resume next week.
The DUP has described the Sinn Féin suggestion as a stunt.
There has been little indication of an improvement in relations between the two parties.
Efforts to restore power-sharing were suspended on 4 July.
Issues that proved intractable then included a proposed Irish Language Act and whether Stormont should remove Northern Ireland's ban on same-sex marriage.
Brexit is also complicating matters, as the DUP could find the 47 members of Sinn Féin, the SDLP and Alliance lined up against it on Brexit issues in what is a 90-member Assembly.
Democratic Unionists have claimed that Sinn Féin intransigence is preventing NI politicians from dealing with growing problems in health, education and the economy.
The DUP responded to criticism levelled by Sinn Féin that they are the ones halting the formation of power-sharing administration.
Senior DUP member Simon Hamilton said the executive should be formed immediately, with a parallel process instigated to deal with the outstanding issues at the heart of the political rift.
Yesterday, Sinn Féin's Stormont leader Michelle O'Neill wrote to the Irish and British governments and leaders of other political parties in Northern Ireland calling for negotiations to resume next Monday,
Ms O'Neill said she did not believe there was a need or public appetite for drawn-out discussions.
Mr Hamilton branded the Sinn Féin move a "stunt".
"It's a stunt by Sinn Féin to deflect away from the growing criticism there is of Sinn Féin because of their failure in helping to restore an executive is having a negative effect," he said.
He rejected the claim that the DUP was failing to implement previous agreements on the matters of dispute.
Mrs O'Neill rejected the claim her letter was a stunt.
"What it clearly is about is trying create a bit of momentum, trying to kick-start a process," she said.
"I have heard James Brokenshire saying that he wants to resume things before the end of the summer, but it needs to happen now.
"We are ready, we are willing."