Independent unionist MLA Claire Sugden has said she will consider taking the job of justice minister if she is offered it.
However, she said no offer had been made by the first and deputy first minister yet.
Earlier, the DUP and Sinn Féin said they are confident that a justice minister will be appointed next week.
On Thursday, the Alliance Party turned down the ministry.
Northern Ireland Secretary Theresa Villiers has said that a justice minister must be appointed by next Wednesday or fresh assembly elections will have to be held.
Ms Sugden met the first and deputy first ministers on Thursday.
"They simply asked me how I felt about things," she told the BBC.
"If an offer is made I will consider it. I have no wish list. I will do what I think is the right thing for my constituents."
SDLP leader Colum Eastwood, who on Thursday announced his party would be going into opposition, urged Ms Sugden not to take the post.
"I think we're beyond the point where these two parties need to get somebody from outside the executive to do that job," he said.
"I think it's a disgrace, it's an issue of their own making of course, because it's more about position-sharing than about power-sharing. We wouldn't take it on that basis, I don't think anybody else should either."
Arlene Foster and Martin McGuinness also held a meeting with Green Party leader Steven Agnew.
He said taking the job would be "problematic".
Sinn Féin leader Gerry Adams was asked if a DUP justice minister would be acceptable to his party.
"We're not going to rise to these suggestions or put-downs," he said.
"We've a job of work to do, that's what we're elected to do and that's what we're resolute about."
Speculation about the justice ministry continues to grow after the Alliance Party's ruling council endorsed the party's decision not to take up the role.
On Friday, Alliance deputy leader Naomi Long said two key issues were not addressed by Sinn Féin and the DUP.
"The issues were around the [assembly] petition of concern and commitment to integrated education, both of which to us are absolutely crucial, one in terms of how governance in Northern Ireland works and the second in terms of how society in Northern Ireland works," she said.
"We're not willing to go in to be a sticking plaster on a self-inflicted sectarian wound that Sinn Féin and the DUP inflict on each other, that's not the role of Alliance."
DUP MLA Simon Hamilton said that he was "very, very confident" that an justice appointment will be made before the deadline.
"We are so confident that we have asked the business committee to convene the assembly next week and we will have an executive, that will include a justice minister, formed," he said.
Speaking on Friday, he also praised Ms Sugden, saying: "I think Claire is a very good assembly member.
"She has the skills and the ability to be a minister."