The move comes amid concerns the Government will compromise its stated impartiality in the region if it enters a confidence and supply deal with the DUP at Westminster.
Ahead of her meeting in London Sinn Féin's leader at Stormont, Michelle O'Neill, said a DUP-Tory deal would not be allowed to undermine the peace process.
Talks with the DUP on a deal to shore up a minority Conservative administration are "progressing well" and the parties have reached "broad agreement" on the principles of the Speech, which will set out the Government's legislative programme for the coming year, according to a senior Conservative source.
A Conservative source said there was so far no deal to announce and that a decision on the timing of any announcement would only be made once an agreement was finalised.
Secretary of State for Northern Ireland James Brokenshire has warned there was "very little time left" to restore a power-sharing executive at Stormont before a 29 June deadline.
The 1998 Good Friday Agreement commits the United Kingdom and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
Eoin Morgan admits to England regrets after dismal Champions Trophy exit
England faltered from 128 for two to lose their last eight wickets for just 83 runs in under 23 overs on a low, slow surface. There's a reason why Pakistan were being termed as "unpredictable" going into the Champions Trophy and they proved it today.
But the other Stormont parties have warned that any deal between the DUP and Conservatives could make restoring power sharing more hard.
Sources told the BBC any public statement about the talks yesterday would have been seen as inappropriate after the Grenfell Tower tragedy.
Negotiations broke up on Tuesday night without an agreement, but Mrs May said the discussions had been "productive".
He spoke out after holding face-to-face talks with Theresa May in Downing Street aimed at kick-starting the stalled Northern Ireland peace process.
The DUP leader said: "There's been a lot of commentary around the issues that we are talking about and it won't surprise anyone that we are talking about matters that pertain, of course, to the nation generally".
Theresa May's plan to govern with the support of a Northern Irish protestant party risks thrusting the province back into turmoil by convincing "hard men" on both sides of the divide to return to violence, former Prime Minister John Major said.
"The UK Government is offering whatever support we can, working alongside the Irish government, as appropriate, honouring our respective commitments in the Belfast Agreement to serve the interests of the whole community in Northern Ireland", he said.