Talks between the Northern Ireland Secretary of State and leaders of the five largest political parties are taking place today and tomorrow.
The meetings are being held in London and Belfast.
It is understood that the focus of Chris Heaton-Harris is to facilitate the return of the Northern Ireland Executive as soon as possible.
Stormont's power-sharing institutions have been dormant for more than 16 months due to a boycott by the Democratic Unionist Party in protest at post-Brexit trading arrangements.
A source at the Northern Ireland Office said that parties will be pressed on their plans for a programme for government for an incoming executive, which would need to be fully costed and within budget.
It is understood that tough spending decisions and revenue raising measures will be required, and officials are currently studying revenue raising measures put forward by departments in Northern Ireland.
The Office of the Secretary of State is believed to be available to work with the parties through the summer on these issues.
Govts need to do more to restore powersharing - Sinn Féin, DUP
Sinn Féin's leader in Northern Ireland said the current "vaccum" is "unsustainable".
"Daily I hear from families, from parents, from people with disabilities, public sector workers, health staff and many others who are facing hardship, uncertainty and unprecedented challenges because we have no executive, no ministers and nobody at the wheel.
"I am clear with the British secretary of state, that for ordinary people, the current vacuum is simply not sustainable."
Ms O'Neill also said there is an onus on the British and Irish Governments to do more, adding that she is determined to work with the two governments, the DUP and all other parties to "find a way forward".
Speaking after a meeting with Mr Heaton-Harris in London, DUP leader Jeffrey Donaldson said that "the ball is in the government's court" and that "unionists just want a fair deal".
He told Mr Heaton-Harris that there was "no solid basis for an executive and assembly" until there were "arrangements to safeguard Northern Ireland's place in the UK, internal market, and our constitutional arrangements are respected".
"The DUP has a mandate to restore the NI Assembly on a basis that unionists as well as nationalists can support. Consensus is the only way forward in Northern Ireland.
"Unionists just want a fair deal. Nationalists would never have been asked to accept the kind of arrangements north-south that unionists are being asked to accept between one part of the UK and another."
Mr Donaldson said the British government committed to taking action to restoring Northern Ireland's place in the internal market, but there had been "a lack of meaningful action".
"We need stable and sustainable devolved government and we need funding for our public services that meet the needs of our people.
"Northern Ireland is a divided society. Quick fixes without solid foundations will do a disservice to those trying to make the NI Assembly work," he added.
SDLP leader Colum Eastwood said there could be "no summer recess on efforts to restore devolution".
Speaking after his meeting with Mr Heaton-Harris, Mr Eastwood said: "People across our communities are experiencing hardship and pain as the impact of the breakdown of democratic governance steadily gets worse.
"People waiting for hospital treatment, families where working parents haven't had a fair pay rise in years, people who can’t afford soaring mortgage costs or childcare bills won’t be getting a break over the next few months and neither should political leaders who have a responsibility to form a government."
Mr Eastwood said he outlined to Mr Heaton-Harris that the SDLP will play a "constructive role in opposition" to re-establish the institutions.
He said the party's priorities include addressing childcare costs, transforming the health service and supporting families in addressing the cost of living.
The SDLP leader said that people are "quickly running out of patience" with progress on these issues.
