Sky's Ireland Correspondent David Blevins reports that DUP leader Arlene Foster is not returning to Belfast on Tuesday as planned, which could suggest a deal is not far away.
The talks with the DUP follow her apology to Conservative rank-and-file lawmakers in a meeting for the party's poor election result.
The loss of her majority meant May has been reaching out to the ultra-conservative Democratic Unionist Party to prop up her Conservative party.
After House Speaker John Bercow was re-elected without challenge, a chastened May quipped: "At least someone got a landslide".
This political uncertainty, as well as fears of another general election if the Conservatives fail to gain the DUP's support, is expected to damage consumer and business confidence, according to Dean Turner, economist at UBS.
May's spokesman said the prime minister, who in March set Britain on a two-year countdown to leaving the EU that included a clean break with the bloc's single market and customs union, was not changing her position on what she wants from Brussels.
One source close to the DUP talks said an agreement "should be wrapped up within 24 hours".
The Daily Telegraph reported cabinet ministers have opened back channel talks to senior Labour lawmakers to secure a cross-party agreement on Brexit.
"We continue to work with all the parties in Northern Ireland and the Republic of Ireland in ensuring that we can continue to put in place those measures necessary to fulfil those agreements, " she said.
Foster will nearly certainly ask for greater investment in Northern Ireland as part of the deal, as well as guarantees on support for pension plans and for winter fuel allowances for older people.
Queen visits London fire volunteers
The renovation project included installation of insulated exterior cladding, double-glazed windows and a communal heating system. Her staff will remain on scene for "days to come" and that the search of the tower would be a "slow and painstaking process".
Ms May faces a hard balancing act: Divisions over Europe helped sink the premierships of Margaret Thatcher, John Major and David Cameron, and many of her politicians and party membership support a sharp break with the EU.
Even the idea of an alliance is complicated, however.
While a deal with the DUP would help May stay in power to open Brexit talks that are due to begin next week, it would also risk destabilizing the political balance in Northern Ireland by increasing the influence of pro-British unionists.
Sinn Fein's Stormont leader Michelle O'Neill said: "I will be making it very clear that any deal between the Tories and the DUP can not be allowed to undermine the Good Friday and subsequent agreements".
The stakes for May are high.
But May appears to be motivated by her desire to guarantee a majority in Parliament for a Queen's Speech - a key event in the parliamentary calendar in which the government lays out its policy agenda for the coming year. If that happens, Corbyn will demand a chance to try to form a government by uniting progressive factors in the House of Commons.
May, who ahead of the June referendum supported remaining in the European Union, has promised to start the formal Brexit talks next week but opponents of a sharp break with the European Union took her woes as a chance to push back against her strategy.
According to the statement issued on Thursday, the European Union and the United Kingdom are set to begin negotiations on Article 50, which was triggered on March 29 and sets out the procedure for withdrawing from the 27-member bloc, reports Efe news.
"It's passing quicker than anyone believes That's why we're ready to start very quickly".
His comments come after the EU's chief Brexit negotiator, Michel Barnier, warned London to "not waste time" and begin negotiations as soon as possible.
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