The Prime Minister and Taoiseach will travel to Northern Ireland later amid growing speculation that a deal to restore the powersharing government is imminent.
Theresa May and Leo Varadkar will meet with Stormont's main political parties as they continue talks aimed at ending the 13-month political stalemate.
A Downing Street spokesman said Mrs May would take part in a series of meetings at Stormont House and encourage Sinn Fein and the Democratic Unionists to resolve their differences.
A spokesman for Mr Varadkar said he and Mrs May would assess the state of play in the negotiations between the parties.
In a sign that the dynamic at Stormont has shifted gears, the Taoiseach has cancelled a scheduled meeting with Welsh First Minister Carwyn Jones in Dublin on Monday in order to head to Belfast.
Downing Street said Mrs May will tell the parties her government is ready to introduce legislation to enable the re-establishment of a devolved executive as soon as possible, if an agreement materialises.
Ahead of the meetings at Stormont, the Prime Minister will visit a local business to meet staff and management.
Northern Ireland has been without a functioning government since January 2017 and several rounds of talks to resolve the crisis have failed.
However, speculation has been growing that a deal between Sinn Fein and the DUP is close.
Both parties publicly acknowledged on Friday that progress had been made.
On Saturday, Sinn Fein's Stormont leader Michelle O'Neill said talks are likely to draw to a close this week.
The DUP/Sinn Fein-led coalition imploded last January amid a row over a botched green energy scheme.
That rift subsequently widened to take in long-running disputes over culture, social issues and legacy.
The main sticking point preventing the restoration of an Executive is the Irish language.
Sinn Fein wants a stand-alone piece of legislation to protect speakers - an Irish Language Act - but the DUP has long insisted it would only countenance new laws if they also incorporate other cultures, such as Ulster Scots.
Finding a compromise resolution to the thorny language dispute that will satisfy both parties is key to breaking the Stormont deadlock.
SDLP leader Colum Eastwood warned that any deal to restore powersharing must end the cycle of political stand-off between Sinn Fein and the DUP.
Mr Eastwood said it is not enough to simply form a new executive.
"The real change necessary is an end to the cycle of two parties who have proved themselves very good at the art of political stand-off, but very bad at the responsibility of government," he said.
"That is the joint DUP/Sinn Fein status quo that must now end."
Mr Eastwood added that when powersharing is restored, focus must return immediately to the threat posed by Brexit, the economy and the crises in the health service and school budgets.