There is a steady dialogue between the two sides that has never stopped at any point.
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 only thing I know is that there is an Article 50 request and we have been preparing ourselves for a long time to start negotiations on that basis".
She reportedly apologised to Tory MPs, accepting personal responsibility for failing to win an outright victory and sacrificing the parliamentary majority she inherited from David Cameron when she became leader after the Brexit referendum a year ago.
The First Minister said she is concerned by the "disregard" shown for the Northern Irish peace process and called for full details of any deal to be made public.
Parliament now "deserves a say", he said, adding that there was "perhaps an opportunity to consult more widely with the other parties on how best we can achieve it".
Without a so-called confidence and supply deal with the DUP, her party risks losing the vote next week on the Queen's Speech. "You folks here make enough mess of your own elections, make enough mess of your own governments, make enough mess of your own affairs".
Demanding a swift start to Brexit negotiations under Article 50 of the European Union treaties, the former Belgian prime minister compared Britain's position to the heroine of Lewis Carroll's Alice In Wonderland, who found herself in a room with many doors and no idea what lay behind them.
May had called the vote early in hopes of strengthening her majority going into talks on exiting the European Union, but instead found herself in negotiations with a small party in Northern Ireland in order to stay in power.
DUP leader Arlene Foster has said she is keen to secure a "frictionless" border with Ireland and has spoken out against a "hard Brexit".
Brexit talks to be delayed?
A Scottish Conservatives spokesman said: "Even for the SNP, Nicola Sturgeon's attack on the Conservative talks with the DUP takes hypocrisy to new levels". Until she does, she and her ministers are on borrowed time.
The meeting will be chaired by the Police and Fire Minister Nick Hurd.
She said there is a real question about whether the UK Government could be an impartial broker in the peace process as outlined by the Good Friday Agreement.
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.
"This new arrangement is very unsettling and people are concerned and anxious about what it may mean, or what promises may be given".
Ministers are likely to have their first political discussion on the issue.
The Northern Ireland-based party is being courted by May to create an alliance to push through the Conservative Party's agenda after a disastrous snap election left May short of a majority in Parliament.