The leaders of the five parties in the Northern Executive will take part in discussions at a meeting of the Party Leaders’ Forum later on Thursday.
The new DUP leader, Edwin Poots, said the meeting could provide "a useful opportunity to ensure there is a smooth transition to changes within the Executive team."
Mr Poots, who was ratified as party leader following an acrimonious meeting last week, has so far declined to name his new ministerial team, instead saying that he will do so when he is ready and denying the delay is due to divisions within the DUP.
However there are concerns that the ministerial changes - and the appointment of a new First Minister - could lead to political tensions and potentially spark a crisis which could threaten the stability of the power-sharing institutions.
The North's Minister for Justice, Naomi Long, warned on Wednesday that "any changes at Stormont obviously create the opportunity for instability" and told the BBC that there was an opportunity "to see instability within the DUP itself reflected in instability in the institutions.
“We still haven’t had a new First Minister appointed. That’s another opportunity for instability and I think all of us are just now awaiting what’s going to happen,” she said.
Under the power-sharing rules in force at Stormont, the Deputy First Minister, Michelle O'Neill, will also cease to hold office once the outgoing First Minister, Arlene Foster, resigns.
Ms Foster has indicated she will step down as once Mr Poots nominates his new team, which will trigger a seven-day countdown for both parties to re-nominate their candidate for each position.
If either party refuses to make a nomination, an Assembly cannot be formed, which could lead to an early election.
There has been speculation that Sinn Féin could seek to use the process to secure assurances from the DUP around sticking points such as the implementation of Irish-language legislation.
On Wednesday Mr Poots said the meeting of the Party Leaders' Forum was an "opportunity" to "affirm the commitments" made in the New Decade, New Approach [NDNA]deal which restored the North's power-sharing Assembly in 2020 "to operate the political institutions on the basis of good faith, trust and mutual respect and reaffirm our commitment to the principles of power-sharing and cross community protection as contained in the Belfast Agreement."
The Forum was created as part of the NDNA agreement to improve collaboration and partnerships and to strengthen the stability of the North’s political institutions.
On Wednesday the North's Minister for Communities, Deirdre Hargey, accused the DUP of "unacceptable and regressive behaviour" after the party's junior minister, Gordon Lyons, did not take part in a scheduled North-South meeting on language issues.
The DUP has boycotted a number of cross-Border meetings in recent months as part of its campaign against the Northern Ireland protocol.
The meeting could not proceed as, under Stormont rules, any meeting with the Government which involves a nationalist Executive minister must also include a unionist counterpart.
“As planned, I was available and ready to chair this afternoon’s North South ministerial meeting on language with Minister Jack Chambers TD,” Ms Hargey said.
“It is totally unacceptable that government business is being hampered by DUP ministers who are failing to attend these meetings where First Minister Arlene Foster is failing to nominate a replacement from her number.
This is the second time the DUP have failed to attend a language sectoral meeting and this continued boycott is unacceptable, futile and cannot continue.
“North-South ministerial meetings are an integral part of the political institutions of the Good Friday Agreement alongside the Executive and the Assembly. They need to be functioning properly with ministers from all parties attending,” Ms Hargey said.
Ms Hargey said on Wednesday night that she was seeking legal advice on bringing a judicial review against DUP ministers who refuse to attend the North-South meetings, saying their action may be in breach of the ministerial code.