Peter Robinson is to be sworn in but Martin McGuinness may not cooperate
The DUP and Prime Minister Gordon Brown have discussed doubts over whether Sinn Féin will disrupt the handover of power between Ian Paisley and Peter Robinson.
An assembly election could be called within weeks if it is not resolved.
Sinn Féin is unhappy at the DUP's veto of devolving policing and justice, and Gerry Adams also met Mr Brown earlier.
Neither party has commented on the meetings, but sources suggest the impending crisis may be waning and a resolution is possible.
The DUP said the meeting was arranged well in advance, with the agenda including issues such as government support for a Bombardier plane contract and a smooth leadership transition between Mr Paisley and Mr Robinson.
Earlier, Sinn Féin described its meeting as a private discussion and Mr Adams left through the back door of 10 Downing Street without commenting.
Sinn Féin is angry at the DUP's veto of devolving policing and justice powers to Stormont, as well as its failure to introduce an Irish language act.
However, the DUP insists it will not negotiate under duress.
Senior government sources have been trying to dampen the sense of an impending crisis - they say all the two parties need is reassurance that the other is serious about devolution, and they believe a resolution can and will be found.
Sinn Féin and DUP leaderships had talks at Stormont on Monday.
It was expected to be a formality on Thursday, that after Ian Paisley stepped down as first minister to be replaced by Peter Robinson, Sinn Féin would nominate Martin McGuinness as deputy first minister.
If Mr McGuinness is not nominated, the two parties have one week to resolve the issue before the Northern Ireland Secretary steps in.
Shaun Woodward could call an election to break the deadlock.