Sinn Féin leaders Gerry Adams, Mary Lou McDonald and Michelle O'Neill are to meet with the UK Prime Minister in Downing Street tomorrow, according to reports.
According to UK media the party's leadership want to speak with Theresa May about her proposed deal with the Democratic Unionist Party (DUP) and the formation of the Northern Executive.
The anticipated deal with the DUP has forced Mrs May to reject claims that the Government will fatally undermine its supposed impartiality in Northern Ireland, in particular in the ongoing process to restore Stormont powersharing.
The 1998 Good Friday Agreement commits the UK and Irish Governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
Sinn Fein's Stormont leader, Michelle O'Neill, said she would raise the issue with the Prime Minister in face-to-face talks in London on Thursday.
Mrs O'Neill said she would discuss her concerns with Taoiseach Leo Varadkar the following day.
"I will be in London and Dublin over the coming days for talks with both Theresa May and the new Taoiseach, Leo Varadkar," she said.
"I will be making it very clear that any deal between the Tories and the DUP cannot be allowed to undermine the Good Friday and subsequent agreements.
"It's imperative that both Governments recommit to the word, spirit and implementation of the Good Friday Agreement if there is to be any prospect of re-establishing the Executive."
Mrs O'Neill added: "Progress will not come from a deal between the DUP and Tories to prop up a Government in Westminster with an austerity and Brexit agenda but through the full implementation of the agreements and an Executive that respects the rights and delivers for all in society."
Talks between the Tories and the Democratic Unionist Party were continuing on Wednesday amid reports that any announcement of a deal may be delayed because of the tragic fire in a London tower block.
Theresa May needs the votes of the DUP's 10 MPs to prop up her minority administration as she hopes to steer government business - including crucial measures on Brexit - through the Commons.
The BBC reported DUP sources who said the talks were going well but it was thought "inappropriate" to make an announcement while events were unfolding at the Grenfell Tower in west London, where at least six have died.
It was reported that diary commitments meant finalisation of any deal could be delayed until next week.
A Conservative source said there was so far no deal to announce and that a decision on the timing of any announcement would have to wait until an agreement was finalised.
Ministers have already said that the Queen's Speech may have to be set back from its scheduled date of next Monday, June 19, because of the ongoing negotiations.
Mrs May is coming under intense pressure to change her approach to leaving the European Union, with predecessor David Cameron among those suggesting a softer stance with a greater effort to seek a consensus.
Talks with the DUP broke up on Tuesday night without an agreement, but Mrs May said the discussions had been "productive".
A senior Conservative source said: "We are making a lot of progress. It's all being done in the spirit of cooperation, with a real focus on strengthening the union and providing stability at this time."
DUP leader Arlene Foster, who travelled to Westminster for talks with the Tories on Tuesday, said she hoped a deal could be reached "sooner rather than later".
The proposed "supply and confidence" deal would see the DUP back the Conservatives in votes on the Budget and confidence motions.
For Labour, shadow business secretary Rebecca Long-Bailey said the prospect of a Conservative-DUP deal was "worrying", telling BBC Radio 4's Today programme: "It would create a lot of instability in terms of the peace process in Northern Ireland."
One of the most pressing issues facing Mrs May is the process of leaving the EU, with Brexit talks set to start in Brussels on Monday.
Former prime minister Mr Cameron said Mrs May would have to change her approach to Brexit as a result of the election.
"It's going to be difficult. There's no doubt about that, but perhaps an opportunity to consult more widely with the other parties on how best we can achieve it," he said at a conference in Poland.
"I think there will be pressure for a softer Brexit," Mr Cameron added, saying that Parliament now "deserves a say" on the issue.
He also suggested that the Scottish Tories led by Ruth Davidson could also add to the pressure on Mrs May to change course.
"There's no doubt that there is a new player on the stage," Mr Cameron said. "Scotland voted against Brexit. I think most of the Scottish Conservatives will want to see perhaps some changes with the policy going forward."
The Times reported that Chancellor Philip Hammond was preparing to fight for the UK to remain within the EU's customs union.
That would help safeguard jobs and trade with EU members, but would severely restrict the UK's ability to strike its own trade deals around the world.
At a joint press conference with Mrs May in Paris on Tuesday night, French President Emmanuel Macron suggested that the door was still open for the UK to remain within the European Union.
"Until the negotiations come to an end, of course there is always the possibility to re-open the door," said the French President. "But let us be clear and organised and once the negotiations have started we should be well aware that it'll be more difficult to move backwards."
Mrs May stressed that Brexit would happen and the timetable remains on course.
She said: "I think there is a unity of purpose among people in the United Kingdom.
"It's a unity of purpose, having voted to leave the EU, that their Government gets on with that and makes a success of it, and we are committed to developing a deep and special partnership with the EU.
"We want the EU to continue to remain strong and we want to continue to cooperate."
With additional reporting from PA