Leading Irish language advocates are seeking assurances the DUP will agree a language act before a new first minister is ratified by Sinn Féin.
Arlene Foster is expected to stand down as first minister as early as tomorrow after Edwin Poots became the new DUP leader last week.
Sinn Féin president Mary Lou McDonald has written to the other leaders asking for an all-party meeting this week.
It is understood she will push for commitments to language legislation before Sinn Féin will agree to ratify any DUP pick as first minister.
If no agreement can be reached on a new first minister, then the Secretary of State will have to call an early Assembly election, most likely in the autumn.
An Irish language strategy, along with a commitment to an Ulster Scots language, heritage and culture strategy, was agreed as part of the New Decade, New Approach (NDNA) deal in January last year.
Irish language group Conradh na Gaeilge (CnaG) said it expects Mr Poots to stand by commitments made in NDNA.
Lagan Valley MLA Paul Givan has been tipped as the DUP pick.
He was partly blamed for the collapse of the devolved institutions in 2017.
His abrupt announcement as communities minister of a cut in funding for Irish language Gaeltacht bursaries two days before Christmas 2016 was described by Sinn Féin as "the straw that broke the camel's back" in relation to Martin McGuinness's decision to resign as deputy First Minister.
Conchúr Ó Muadaigh, advocacy manager for Conradh na Gaeilge (CnaG), said it expects Mr Poots to stick to NDNA.
"Last year the institutions were re-established on the basis of the full implementation of the New Decade New Approach Agreement," he said.
"All parties who entered the power-sharing executive, including the DUP, signed up to this agreement in all of its parts, including the British and Irish Governments.
"The Irish language community, and I would imagine the public in general, fully expect all parties to implement that agreement.
"Irish language legislation was a core component of that agreement.
"Any attempt to renege or retreat from that agreement would be a retreat from the very principles on which the institutions were returned.
"Resolute action for the Irish language was a fundamental part of the Good Friday Agreement."
CnaG has launched a legal challenge against the Executive over its failure to implement a strategy more than four years after a landmark court ruling.
Meanwhile, several DUP members are expected to resign from the party following disquiet over how Mrs Foster was removed as leader.
Mrs Foster has described the party's vision under Mr Poots as "nasty" and said she will resign from the DUP once she leaves office.
If Mr Poots appoints a new ministerial team tomorrow she will step down as first minister.
Economy minister Diane Dodds, education minister Peter Weir and junior minister Gordon Lyons are expected to be ousted.
North Antrim MLA Mervyn Storey, new DUP deputy leader Paula Bradley and Strangford MLA Michelle McIlveen have been tipped to replace them, however, North Antrim MLA Paul Frew's name has also been mooted as a possible minister.