Some opposition politicians say that stance is no longer acceptable, with some in her own party pressing May to soften her position and focus on saving jobs after Britain leaves.
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.
For Brussels, a concern with starting talks on such models would be that Brexit supporters might end up blocking them, raising the risk of time running out to get any deal: "Would you". There is a steady dialogue between the two sides that has never stopped at any point.
May does not necessarily need a firm deal from the DUP before opening parliament and might hope that she would receive the necessary backing anyway.
"I'm not going to give a blow by blow account of how we propose to take that discussion forward", he said. "We want to see any deal between those two parties reflect the wishes of all of the people of Northern Ireland, not just one section of the community".
May is holding talks Thursday with other Northern Ireland political parties amid warnings the expected DUP deal will undermine the peace process.
A deal between the Conservatives and the Democratic Unionist Party to prop up a minority government may not be reached by the time the Queen's Speech goes ahead next week, it has been revealed.
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"Talks with the DUP have been progressing well and there is broad agreement on the principles of the Queen's Speech", said the source.
Before the Mansion House dinner was cancelled because of the fire, finance minister Hammond had been due to tackle fears among the financial elite that May's insistence that "no deal is better than a bad deal" would cost them business.
"We would restore faith in politics if we could show that this parliament can at least function in presenting a view in the national interest which would command a majority on a cross-party basis", said veteran pro-European Conservative lawmaker Ken Clarke.
The EU's chief Brexit negotiator, Michael Barnier and the UK's Brexit minister, David Davis, will meet in Brussels on Monday (19 June), kicking off negotiations likely to take nearly two years.
A week after May lost her majority in an election she had called in the hope of strengthening her hand in the talks, some fellow Conservatives want her to focus more on limiting the damage to business and less on cutting immigration and other ties to the European Union when Britain leaves the bloc in March 2019.
But some opposition politicians say that May can no longer stick to her stance for a clean break with the European Union, characterizing her election bid as a poor gamble that has left Britain a laughing stock.
"Look at what the Tories (Conservatives) have managed to do to the United Kingdom in the space of just one year, firstly calling a divisive and reckless European Union referendum. then having lost that gamble pursuing a hard Brexit path", Scotland's first minister, Nicola Sturgeon, said.