The British Government has made parliamentary time available to reinstate Stormont powersharing next week.
Northern Ireland Secretary James Brokenshire urged a spirit of compromise as local politicians tried to piece together a deal.
The Leader of the House of Commons said she was "hopeful" of good news.
Westminster legislation would be needed to enable the formation of a ministerial Executive if the DUP and Sinn Fein reach a solution.
Mr Brokenshire said: "Now is the time for the parties to look beyond their differences, harness a spirit of compromise and reach agreement."
He has warned that he may be forced to pass a budget to enable continued spending on public services in Northern Ireland if no deal is reached between the DUP and Sinn Fein.
House of Commons business for next week was unveiled by Commons Leader Andrea Leadsom.
She said: "We're very hopeful that there may be some good news coming from Northern Ireland that might enable legislation to recreate the Northern Ireland Executive.
"We always wait hopefully that that will be the case."
Mr Brokenshire said he would be reluctant to see more political decisions made at Westminster rather than Belfast.
"But if a deal is not reached imminently, that greater intervention - beginning with Westminster legislation to set a 2017/18 budget for Northern Ireland - risks becoming inevitable.
"This would be a big step backwards, a step I do not want to have to take.
"But I will not shirk from my ultimate responsibility for good governance and political stability in Northern Ireland."
The Executive has been in cold storage for most of the year after a major fall out between the DUP and Sinn Fein over a botched green energy scheme.
It prompted the resignation of late deputy first minister Martin McGuinness and collapse of the institutions.
Disputes over the place of the Irish language and other identity issues have bedevilled efforts to rebuild a consensus.
Republicans and the large unionist party have been engaged in intensive discussions for weeks.