Many in Northern Ireland, especially the Loyalist community, see this DUP-Conservative arrangement as a good thing if the deal is signed today, as it may highlight the areas of Northern Ireland that need investment. May and Foster later left through different exits.
According to BBC, a deal between both parties was supposed to be announced on Wednesday thereby helping May form government in the United Kingdom after her party emerged as the largest party in the recently concluded elections but failed to win a majority.
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.
European Parliament leaders laid into May and called for Britain to say when negotiations would start.
He said: "I'm sure we all look forward to welcoming the Queen's Speech just as soon as the coalition of chaos has been negotiated".
British Prime Minister Theresa May sits with Foreign Secretary Boris Johnson as she holds the first Cabinet meeting of her new team inside 10 Downing Street, in London, Monday June 12, 2017.
Ms May made clear the Brexit negotiations would begin on schedule despite the political uncertainty at home.
"We stand at a critical time with those Brexit negotiations starting only next week - I think that stability is important".
It is expected they will also talk about Brexit negotiations which are due to start next Monday.
In another intervention Tuesday, former Conservative prime minister Sir John Major warned against a pact between May and the DUP.
The DUP and Sinn Fein - who have ruled Stormont together for the past ten years - wiped out the more moderate Ulster Unionist Party and SDLP last week.
But a press conference this evening, when asked about Major's warning to the Tories, May said her government still supports the Belfast agreement and the peace process in Northern Ireland.
"Yesterday Emmanuel Macron, the new French president, spoke about an open door, he said if Britain is changing its mind it will find an open door", Verhofstadt told the European Parliament.
The embattled 60-year-old premier said she had served the Conservative Party since the age of 12 and will continue to do so as long as she is wanted.
"My main concern is the peace process".
Senior British minister and prominent Brexit campaigner Michael Gove said on Tuesday that Britain will leave the EU customs union, which guarantees tariff- free trade within the bloc but prohibits members from striking third-party trade deals.
As talks go on, the European Union unveiled plans to give itself new powers over London's banking business after Brexit, in what could be a blow to the city's supremacy as a global financial hub.