Ken Clarke, who is Father of the House as the longest serving MP in the Parliament, told the Today programme on Wednesday morning that "you can not carry out this negotiation on the basis that every aspect of this is going to be negotiated with the DUP. and then you have to get the entire Conservative Party to agree with it".
She also gave a glimpse into the issues on the table, saying Brexit, counter-terrorism and "doing what's right" for the Northern Ireland economy were among the key issues being thrashed out.
Conservative leader May lost her parliamentary majority in last week's election and is now desperately seeking the backing of the 10 MPs from Northern Ireland's ultra-conservative Democratic Unionist Party (DUP).
Without the DUP's support, May can not be sure of doing so.
Discussions in Westminster are continuing without Theresa May after she left for Paris for a pre-arranged meeting with newly elected president Emmanuel Macron.
And as protracted negotiations between the ruling Conservative Party and a small Northern Irish party remain unresolved, a meeting with another party from the province is set to add further confusion to proceedings. Her spokesman insisted her position on Brexit remained unchanged but Scottish Conservatives were pushing for her to move the focus onto economic growth and away from immigration, sources in the Scottish branch of the party 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".
The decision to announce a new date for the Speech, two days later than its scheduled date of June 19, was made after Mrs May's regular audience with the Queen on Wednesday.
Two policemen injured in Srinagar militant attack
The Indian Army is retaliating strongly and effectively. "As he returned to his home, he was shot by the militants", they said. A series of attacks were carried out by militants in Tral, Anantnag, Pulwama, Padgampora and Sopore in Kashmir.
The prime minister had hoped to be in the French capital with a strong popular mandate for a "hard" Brexit.
Conservative Party talks with the DUP are expected to be completed today.
Meanwhile, the chief European Union negotiator has told the Financial Times that Britain that the clock was ticking on Brexit talks, and that Britain should be wary of further delays.
Conservative Prime Minister Theresa May first triggered the Article 50 mechanism to leave the bloc nearly three months ago, with formal discussions due to begin on 19 June.
Mr Drakeford added: "As John Major has said, if this turns out simply to be cash for votes, then that is a very, very undignified position for the United Kingdom government to have put itself in".
May plans a clean break from the EU, involving withdrawal from Europe's single market and customs union and limits on immigration from the EU.
As European leaders tried to fathom exactly how Britain would begin the negotiations, German Finance Minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain.
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