The Northern Ireland Secretary and Tánaiste are meeting the five main political parties at Stormont over the restoration of power-sharing.
After the meetings, Simon Coveney and Julian Smith will have to decide if they are to publish the agreed position of the Irish and British governments on how to resolve the issues that have caused political stalemate.
If both ministers decide to press ahead and publish their proposals, it will be a significant initiative.
Mr Smith has already indicated that if no agreed deal is in place by next Monday, 13 January, he may call fresh Assembly elections.
The latest series of meetings with the parties began shortly before 4pm at Stormont House and look set to go on late in to the night.
The latest developments at Stormont came as British Prime Minister Boris Johnson, addressing the Commons, urged the Northern Ireland's politicians to "take responsibility" and get the institutions up and running again.
The last DUP/Sinn Fein-led coalition government collapsed in January 2017 over a row about a botched green energy scheme.
That dispute subsequently widened to take in more traditional wrangles on matters such as the Irish language and the legacy of the Troubles.
Proposed legislative protections for Irish language speakers and reform of a contentious Stormont voting mechanism - called the petition of concern - have been the crucial sticking points in the most recent talks process, which got under way following the UK general election.
Sinn Féin has previously demanded a stand-alone Irish Language Act as a prerequisite of any deal to restore devolution.
The DUP has expressed a willingness to legislate to protect the language, but only as part of broader culture laws that also include the Ulster Scots tradition.
The long-running dispute has boiled down to whether new laws are contained in a stand-alone bill or as part of a wider piece of legislation.
Additional reporting PA