May will meet DUP leader Arlene Foster in London on Tuesday.
It follows warnings - including from former prime minister Sir John Major - that the Government will compromise its stated impartiality in the province if it enters a confidence and supply deal with the DUP at Westminster. "And the danger is that however much any government tries, they will not be seen to be impartial if they are locked into a parliamentary deal at Westminster with one of the Northern Ireland parties".
Irish nationalist party Sinn Fein said the prospect of a British agreement with the DUP was causing anxiety and fear.
A failure to gain support from the DUP would risk the Queen's Speech - which details the government's legislative plans - being voted down next week, and Mr Corbyn has said Labour will be pushing hard for that outcome.
Lord Hain, who was Northern Ireland secretary from 2005 to 2007, warned that the situation is "very damaging" at a time when sensitive talks are under way over the restoration of powersharing at Stormont.
"I think change is brought about, certainly in Northern Ireland, by persuasion, by people working together and the best way actually to achieve these is to get the Northern Ireland Assembly back up and running, and I hope that will also be possible".
"Northern Ireland's political leaders now have it in their hands to take control and shape a brighter future for everyone in Northern Ireland".
Sources also told the BBC that both parties were close to reaching an agreement so that May could form the government but the fire at Grenfell Towers in London made an announcement on the deal on Wednesday "inappropriate".
Premarket: Growth worries push stocks lower, Fed hike lifts US dollar
KEEPING SCORE: Japan's Nikkei 225 stock index fell 0.2 percent to 19,838.86 and South Korea's Kospi sank 0.6 percent to 2,358.66. The eurozone currency plunged to 1.1143 against its American counterpart on Thursday, the lowest level in a fortnight.
Earlier, Andrea Leadsom, leader of the lower house of parliament, said the government had agreed with Queen Elizabeth, who reads out the new government program, that the "state opening of parliament will take place on 21 June 2017".
"The main concern is going to be that if there is a Conservative-DUP deal, then can the British government continue to play the role of a honest broker in the restoration of a Northern Ireland executive?" said Simon Usherwood, senior politics lecturer at Surrey University.
A "Brexit election" that left UK Prime Minister Theresa May without an overall majority has forced her into a precarious alliance with the far-right Democratic Unionist Party, who are deeply opposed to gay rights and abortion.
Former Prime Minister John Major said he was concerned a deal with the DUP could thrust the province back towards violence almost two decades since a USA -brokered peace deal brought peace to Northern Ireland.
He also suggested that the Scottish Tories led by Ruth Davidson could also add to the pressure on Mrs May to change course.
The Times reported that Chancellor Philip Hammond was preparing to fight for the United Kingdom to remain within the EU's customs union.
Meanwhile, the chief European Union negotiator has told the Financial Times that the clock is ticking on Brexit talks, and that Britain should be wary of further delays.