Micheál Martin is expected to meet some of the main parties at Stormont on Wednesday during a visit to Belfast.
It will be the tánaiste’s (Irish deputy prime minister’s) first trip since last month’s local government elections.
Sinn Féin is now the largest party in local government and the assembly for the first time.
Stormont’s power-sharing executive collapsed last year as part of the Democratic Unionist Party (DUP) protest against post-Brexit trading rules.
The party has also blocked the functioning of the Northern Ireland Assembly.
They were speaking after meeting the head of the civil service to discuss the ongoing governance gap.
Mr Martin commented that it was “significant” that the main political parties were talking about additional funding being required if power-sharing is restored.
Sinn Féin vice-president Michelle O’Neill is still in the US so the party is expected to be represented at the talks by Conor Murphy.
Ms O’Neill travelled to Washington on Monday to meet senior US officials and members of Congress to discuss the political situation in Northern Ireland following the outcome of the council elections.
The party won 144 council seats at the poll – a rise of 39 on its 2019 showing.
However Ms O’Neill has yet to take up the position as first minister due to the ongoing boycott by the DUP.
With the election results still being digested and no sign of Stormont returning, Micheál Martin and the parties have much to discuss.
But the cast list is more threadbare than he would have wanted.
Sinn Féin’s Michelle O’Neill is on a visit to the US, while DUP leader Sir Jeffrey Donaldson and SDLP leader Colum Eastwood are both in London.
Sinn Féin will send Conor Murphy instead. Mr Eastwood will talk to the tánaiste by phone. The DUP says Sir Jeffrey may do so too.
That means that only three of the five main Stormont parties will attend in person.
‘People deserve an executive’
Speaking ahead of the visit, Mr Martin said he hoped to engage with all the parties and his message would be that the people of Northern Ireland deserved devolved government.
“I’ve been a consistent believer that when people vote in an election they deserve to have their public representatives representing them in a parliament, in an assembly in this case,” he told a media at the Bloom Festival in Dublin.
“Secondly, I think the Windsor Agreement did address very, very comprehensively many of the issues that the DUP and the UUP and others had raised in respect of the free movement of goods from Great Britain into Northern Ireland and tremendous progress was made on that.
“I will be listening as well to hear different perspectives and our objective is, with the British Government and with all of the parties, ultimately is to get the assembly and the executive restored.”
Wednesday’s meeting comes as UK Prime Minister Rishi Sunak prepares travels to Washington for trade talks with US President Joe Biden.
The White House said the pair would also discuss the situation in Northern Ireland.
Also on Wednesday, Stormont parties are expected to hold another of their now regular meetings with the head of the civil service Jayne Brady. where governance and fiscal gaps are expected to once again lead the agenda.