The meeting is taking place to see if an alliance can be created to push through the Conservative Party's agenda after a disastrous snap election left her short of a majority in Parliament. "I think it's unlikely there will be any announcement today", a DUP spokesman said.
"Although a deal would make parliamentary votes easier I'm not convinced it is absolutely necessary", he said.
May said on Tuesday that talks with the DUP had been productive - a view shared by DUP leader Arlene Foster - and that Brexit negotiations would begin as planned next week.
May will also be reliant upon the 10 lawmakers from the Eurosceptic DUP, who would help her edge past the 326 votes needed in parliament to avoid the government collapsing.
Sinn Fein, SDLP and the cross-community Alliance have all also already made clear that Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore power-sharing at Stormont due to a perceived conflict of interest caused by the deal.
"This new arrangement is very unsettling and people are concerned and anxious about what it may mean, or what promises may be given".
"So there is a lot of anxiety and a lot of fear out of what is being discussed".
"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".
Talks between the DUP and the Tories are set to continue again tomorrow.
MPs returned to Westminster on Tuesday for the new parliamentary session, after May spoke at a crunch 1922 committee meeting in which she apologised to Tory backbenchers for the party's election performance.
"I can't negotiate with myself", was Michel Barnier's response, who's the EU's chief Brexit negotiator. "It's passing quicker than anyone believes That's why we're ready to start very quickly".
"We never put timescales on when we expect a deal to be done and I'm not going to start now".
France's Macron said the EU's door was still open for Britain as long as the negotiations were not finished, but that it would be hard to reverse course.
May is under pressure to take on a more cross-party approach to the negotiations surrounding Brexit.
"We are impatiently waiting for the negotiating position of the United Kingdom gov (ernment)".
Liberal Democrat MP Alistair Carmichael said: The Conservatives can not go from weak and wobbly to business as usual in three days. It is the only way to unite the country and strengthen our bargaining power with the EU.
The draft law would empower Europe to decide if post-Brexit London has the right to host financial market "clearing houses" that deal in euros, the EU's single currency.
With formal European Union divorce talks due next week, May heads to France on Tuesday to meet Emmanuel Macron, who last month swept to victory in its presidential election. They will announce joint plans to fine social media companies such as Facebook, Twitter and Google if they fail to remove extremist content from their websites.