The former justice minister has said she has no list of conditions which she would want to have met before taking up the post again.
Independent unionist Claire Sugden (a relative newcomer to the Assembly) had taken up the post last May, making her the only other MLA in the Sinn Fein-DUP coalition government.
She was asked late on Tuesday night (two days after MLAs returned to Stormont to begin discussions on resurrecting the government) whether anyone had approached her regarding taking the role on again.
“Not yet,” she replied.
As to whether she would take it if approached, she said: “I’d have to be convinced that the two parties have sorted out their differences.
“But I would like to finish the job I started.”
She added: “My assessment of why Sinn Fein brought down the government is I think the DUP were arrogant, in the sense they [were] the largest party, they could do things in their own time – all those things.
“And I think they did forget they were partners in government. And I think if we’re able to move forward there needs to be some demonstration of that; ‘humble pie’, I think some members of that party have described it as. I don’t disagree with that.”
Her predecessor as justice minister, David Ford, had told the News Letter on Friday that someone from his party might consider taking up the role again, after it effectively abandoned the post after the 2016 election.
But he said that in order to agree to that, Alliance would have to be given some concessions, such as on things like the promotion of integrated education.
The News Letter quizzed Claire Sugden if she had any demands of her own.
“I’m realistic – I’m one member in a 90-seat Assembly ... I don’t have a list of demands, because I don’t think I’m in a position to do that.
“My one demand, which is probably no different to what it was last year, is I want to be able to do my job.”
She said she took it on last year because it was an opportunity for her East Londonderry constituents to gain a representative who had “a seat at the Executive table”.