Speculation has mounted that an agreement will be hard to reach due to the deal now being negotiated between the DUP and Conservative Party to support the Tory government.
It comes amid concerns the Government will compromise its stated impartiality in the region if it enters a confidence and supply deal with Mrs Foster's party at Westminster. I am wary about it.
DUP sources have told the BBC an announcement on a deal with Tories had been delayed because of the unfolding tragedy of the Grenfell Tower blaze.
The Conservative source said both parties were "committed to strengthening the union, combating terrorism, delivering Brexit and delivering prosperity across the whole country", and that Northern Ireland would get a funding boost.
Ms May is now engaged in talks with the Democratic Unionist Party over a so-called "confidence and supply" arrangement that give the Conservatives a majority in the House of Commons and the ability to form a government.
Theresa May has signalled she is "confident" of getting the Queen's Speech through the Commons whether or not a deal is reached with the Democratic Unionists (DUP) by the State Opening of Parliament next week.
SDLP Leader Colum Eastwood said: "The context in which the talks process is now being asked to operate in could have very serious consequences if there is any suggestion of a back room deal with the DUP".
DUP leader Arlene Foster and deputy leader Nigel Dodds arriving at 10 Downing Street for talks.
The Northern Ireland secretary, James Brokenshire, will also be at the Downing Street talks which will build on political discussions that took place Monday in Belfast.
Adams added: "We will oppose any deal which undermines the Good Friday agreement".
At a joint press conference with Mrs May in Paris on Tuesday night, France's President Emmanuel Macron suggested the door was still open for the United Kingdom to remain within the European Union.
The DUP leader said: "There's been a lot of commentary around the issues that we are talking about and it won't surprise anyone that we are talking about matters that pertain, of course, to the nation generally".
"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", she said in a statement.
But the other Stormont parties have warned that any deal between the DUP and Conservatives could make restoring power sharing more hard.