May is under pressure after the Conservatives lost their parliamentary majority in Thursday's election.
Britain's best-selling Sun newspaper said senior members of the party had vowed to get rid of May, but would wait at least six months because they were anxious that a leadership contest could propel Labour leader Jeremy Corbyn into power. She is seeking a so-called confidence and supply deal, which would involve the DUP supporting the Conservatives on key votes but not joining a formal coalition. He said it was impossible to predict whether she would still be prime minister at the end of the year.
The latest leadership speculation comes a day after two of May's closest advisers, her joint chiefs-of-staff Fiona Hill and Nick Timothy, resigned amid recriminations about their controlling management style.
The Conservatives won 318 seats - eight less than it needed in order to secure a majority.
DUP leader Arlene Foster with MPs at the Stormont Hotel in Belfast.
"The talks so far have been positive". Beleaguered British Prime Minister Theresa May was working to fill out the ranks of her minority government Saturday after an election that proved disastrous for her Conservative Party and complicating for Britain's exit from the European Union.
Senior Conservatives said there was no longer support in Parliament for a so-called "hard Brexit" after the party saw its Commons majority wiped out.
Kenny also "noted the absence of any nationalist voice in Westminster", after Northern Ireland's Social Democratic and Labour Party (SDLP) lost its three seats in Thursday's election.
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But he said Ireland was anxious for the Brexit talks to go ahead despite the turmoil in London, and for the deal that they produce not to damage peace in Northern Ireland.
"But you've got to convince them of your credibility and that you can move from protesting about the government to being in government".
"May won't be able to make any compromises because she lacks a broad parliamentary majority", he said.
They include 22 new female Labour MPs - taking the total on the opposition benches to 119 - two new disabled MPs and two new Sikh MPs, including the first turbaned Sikh and the first woman to be elected from the UK's over 400,000-strong Sikh community.
Less than a year after May was propelled into Downing Street following Britain's surprise referendum decision to leave the European Union, party insiders were placing bets on how long she could last. "I just don't see how she can continue in any long-term way".
Elmar Brok, a German conservative and the European Parliament's top Brexit expert, told the Ruhr Nachrichten newspaper talks would be complicated by May's formation of a minority government.
If the whole Labour party comes together, using our bigger presence in parliament to harry, harass and harangue the Tories with fresh intensity and a singularity of objective, we can take them apart.
In another sign of the dangers facing Mrs May, Sunday papers reported that Boris Johnson was either being encouraged to make a leadership bid in an effort to oust her, or actually preparing one - a claim dismissed as "tripe" by the Foreign Secretary. "There's a possibility of voting it down and we're going to push that all the way", he explained.