The DUP and Sinn Féin will continue trying to find a candidate to fill the contentious justice ministry with the deadline for creating a new executive inching closer.
The assembly is due to meet on Wednesday when members must appoint ministers to the executive departments and establish statutory committees.
Chairpersons and deputy chairpersons for the statutory and standing committees will also be appointed.
Secretary of State Theresa Villiers has said ministers must be appointed by Wednesday or fresh elections would have to be called.
There was seemingly little progress over the weekend on the issue of the justice ministry.
Alliance had been expected to take the portfolio as it has since the devolution of policing and justice powers in 2010.
However, David Ford's party decided to snub the DUP and Sinn Féin's invitation after their rejection of proposals to boost integrated education and curb the use of petitions of concern.
After receiving the support of party members at a specially convened meeting last week, Mr Ford reiterated his position that the party could not nominate one of its MLAs for justice minister's role.
His colleague, east Belfast assembly member Naomi Long said the party's proposals "would have radically changed Northern Ireland".
"Given the DUP and Sinn Féin response to those proposals, the view of leadership was that we could not recommend an Alliance MLA to take the Justice Minister role, and that view was endorsed," Ms Long said.
"Whether in government or in opposition, we will not be deflected from delivering ambitious change for our community and it is clear that Alliance is energised about progressing that agenda."
A further round of negotiations involving Alliance and the two largest parties is likely this week.
Independent unionist Claire Sugden, who has been linked to the justice job should Alliance refuse, has said she would consider an offer.
Green Party assembly member Steven Agnew has also not ruled himself out as a potential holder of the politically sensitive post if the Alliance Party refuses to retake the job.
However, he said significant changes would be required on the proposed DUP/Sinn Féin programme for government.
Meanwhile, the former leader of the SDLP, Alasdair McDonnell, has said his party made the "right decision" by following the Ulster Unionists into opposition.
Mr McDonnell said the SDLP sacrificed a great deal to keep peace and stability.
"For 18 years the SDLP has worked diligently keeping the various agreements," Mr McDonnell told the BBC's Sunday News.
"We felt that getting peace and stability here was absolutely vital and we sacrificed a lot to do that. It had come to a point where basically the two larger parties were treating smaller parties, particularly ourselves and the UUP, like a doormat.
"It wasn't acceptable and I think he (Colum Eastwood) made the right decision."
