May is due to meet the leaders of all five Northern Ireland political parties, June 15, in an effort to try and form a consensus over power-sharing, following the fallout between Sinn Fein and the DUP in January, when Sinn Fein's Martin McGuinness resigned as deputy First Minister, throwing the executive - the devolved government - into chaos.
The meetings came as time is running out for the parties to reach an agreement on restoring devolved government to Stormont, with the Government set to resume direct rule from Westminster if there is no deal by June 29.
The pact with the DUP had been expected to be sealed yesterday after the prime minister said she had made significant progress in talks.
The Conservatives are having to rely on the support of 10 DUP MPs after they fell eight seats short of winning an overall majority at the general election.
Mrs May stressed Brexit would happen and the timetable remains on course.
Ms O'Neill said: "We made very clear the the Prime Minister that any deal between herself and the DUP can not undermine the Good Friday Agreement, it can not undermine the joint nature of the office".
"We want to know what is in the deal they are offering to the DUP and we want to know when it is going to be put before Parliament", he said.
Gerry Adams has warnedTheresa May that her possible deal with the DUP is playing "fast and loose" with her government's commitment in the Good Friday agreement to be impartial.
Sinn Fein's Northern Irish Assembly leader Michelle O'Neill will be among the guests, and issued a statement flagging her concerns with May over a "confidence and supply" deal with the Democratic Unionist Party.
"We have worked as a party with the DUP before and those are productive talks".
However, the source added that a full deal on the government's programme wasn't required before the opening of Parliament, adding that there would be "steady dialogue" with the DUP.
"The SDLP are clear that any deal struck must not hinder cross-community confidence in our politics".
Details of the DUP's wishlist have been kept secret but it favours a "soft" Brexit and wants to avoid bringing back border controls between Northern Ireland and the Republic.
The DUP source told BBC assistant political editor Norman Smith the two parties were now finalising the "terms and conditions" of an agreement after Mrs May and DUP leader Arlene Foster met on Tuesday.
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