Nearly two weeks after the election, Conservatives have failed to secure a "confidence and supply" agreement with the Democratic Unionist Party to shore up Mrs May's minority administration.
Following talks in Downing Street with new Irish Prime Minister Leo Varadkar, Mrs May said the terms of any arrangement between the Conservatives and the DUP would be made public once they were agreed.
A DUP source told the Press Association that talks with Mrs May's Conservatives "haven't proceeded in a way that the DUP would have expected" and cautioned that the party "can't be taken for granted".
A delegation led by UK Brexit secretary David Davis will meet the EU chief negotiator Michel Barnier and his team in the European Commission's Berlaymont headquarters in Brussels today for discussions. We would have to work out what that looked like.
Mrs May was forced to seek support from other parties after the snap election on June 8 left her nine MPs short of an overall majority in the House of Commons.
The so-called confidence and supply agreement means that the supporting party will back the government in motions of confidence by either voting in favor or abstaining, while retaining the right to vote otherwise in matters of conscience.
If the PM was to lose a vote it could bring down her Government, but Mr Grayling replied: "I am not pessimistic about this".
"We are having good, constructive discussions and I am confident we will reach a sensible agreement".
The start of Brexit negotiations in Brussels underline the urgent need to restore Northern Ireland power-sharing, Ireland's foreign minister has said.
It is thought the DUP is asking for more investment for Northern Ireland as part of the price of its support, and the party also wants the retention of the triple lock guarantee on pensions and winter fuel allowances for older people. I think we will have a sensible arrangement.
"Theresa May has no mandate for the direction she is taking the country".
As he travelled to Belfast to participate in negotiations for the first time, Simon Coveney pledged to "spare no effort" in the process to salvage the crisis-hit institutions at Stormont.
Prime Minister Theresa May will tomorrow push ahead with her post-election plans, despite failing to reach a deal guaranteeing her ability to govern.