British Prime Minister Boris Johnson has accepted an offer from Taoiseach Leo Varadkar to meet to discuss Brexit and Northern Ireland.
A spokesperson for the Taoiseach said contact is under way between both sides to work out the details surrounding the visit.
"The Taoiseach has invited the British Prime Minister to Dublin for talks on Northern Ireland and Brexit. Their offices are in contact to agree a date for these talks in the coming weeks."
In a statement, the spokesperson said the meeting would give both sides a better understanding of their respective positions.
However, the statement reiterated that the backstop and the Withdrawal Agreement are not up for discussion.
It said any discussions on changes to the political declaration would occur between the EU and the UK.
Mr Johnson has insisted up to now that he would not meet EU leaders for talks until the backstop was scrapped.
It comes after the Taoiseach and Mr Johnson spoke over the phone nearly two weeks ago in a conversation described as friendly and warm.
However, the leaders remain at odds over the backstop.
Mr Varadkar told Mr Johnson that the backstop was needed because of decisions taken by the UK as it leaves the European Union.
But Mr Johnson insisted that the backstop - the insurance policy to avoid a hard border - must be abolished if there is to be smooth exit from the EU.
Feargal Purcell, a former government press secretary, has said the meeting that is being planned is "critical" even if both are refusing to budge on the backstop.
Speaking to RTÉ News, he said there is still time in relation to Brexit. It is essential, he said, that the Irish Government uses all the time it has in relation to the "dialogue that can continue".
He also said that the long-term relationship between the two countries is extremely important.
A prime minister and a taoiseach should always be talking regardless of the broader economic and trade situation, he added.
Meanwhile, Minister for Agriculture Michael Creed has said he was aware contact was being made behind the scenes.
Speaking at the Tullamore Show in Co Offaly, the minister said: "Dialogue in any difficult situation is the way forward. Megaphone diplomacy only goes so far.
"I think they have had a very useful first engagement by way of telephone and I know it is planned to have those discussions at the earliest possible date," he added.
He said he was unaware where or when the meeting would take place.
Current state of Anglo-Irish relations was 'not good'
Former taoiseach John Bruton has said a no-deal Brexit is the most likely outcome, as the UK considers its next steps in advance of the 31 October deadline.
Speaking on RTÉ's This Week programme, Mr Bruton said the current state of Anglo-Irish relations was "not good", and the two nations were "in profound disagreement".
He said the UK has not resolved the two commitments it made "one to [the] Good Friday [agreement] and the other to Brexit".
"I think it's for them in the first instance to come forward with proposals on this which they haven't done. In the absence of such proposals there is a difficult relationship at the moment."
He urged the Taoiseach to "stay calm and quiet and wait". He said the Taoiseach had the full support of the European Union.
"If there are any constructive suggestions from Britain, he should respond constructively to those, but to recognise that given this is a British dilemma, it is for Britain to come forward with its own ideas."
"At the end of the day Britain has to have ownership of the solution, but if they have not come forward with any ideas, they are not going to have ownership of it. They must be encouraged to confront these ideas themselves."
Asked whether compromises should be put forward by the EU to end the current impasse, Mr Bruton said "you can negotiate with somebody who wants to negotiate with you ... I don't know whether the EU has an interlocutor in Boris Johnson who wants to negotiate with it."
"At the moment he's setting preconditions, which suggests that he's not interested in negotiation, and if that's the way it is there's nothing that can be done."
"There is no point in making offers to someone who doesn't want to negotiate with you in a serious fashion" he said.