The British Prime Minister Theresa May has met with Northern Ireland's five main parties, as a deadline to form a power-sharing executive at Stormont looms.
Ms Foster, who travelled to Westminster for talks with the Tories on Tuesday, said she hoped a deal could be reached "sooner rather than later".
Northern Ireland is now without a government, after a surge in support for Sinn Fein at Northern Irish Assembly elections earlier this year left nationalist parties holding a majority over unionist ones the first time.
Sky sources say a deal was unlikely to be unveiled today, given the fatal fire at Grenfell Tower in west London.
The source confirmed there was no need for a deal on a so-called "confidence and supply" arrangement to be sealed in order to press ahead with the Speech, and said Mrs May wanted the Government to "get on with its business".
O'Neill said she would meet both May and new Irish Taoiseach Leo Varadkar in the coming days.
Ahead of the meeting with May, Sinn Fein Stormont leader Michelle O'Neill said that any deal between the Conservatives and the DUP in Westminster can not be allowed to stand in the way of the Good Friday Agreement, which sets out the power-sharing process in Northern Ireland.
The DUP won 10 seats in the UK Parliament in last week's election, enough to provide May, whose Conservatives won 318 seats, with a thin majority in the 650-seat parliament.
Talks with the DUP broke up on Tuesday night without an agreement, but Mrs May said the discussions had been "productive".
But instead an extended hold-up looked likely amid reports that the Treasury needed time to consider costs - with the party said to want £1billion in tax breaks for Northern Ireland.
A senior Conservative source said: "We are making a lot of progress".
He warned that a deal between the Conservatives and DUP would be in breach.
The prime minister, he said, has also "just totally ignored the will of the people of Northern Ireland in terms of Brexit", he added.
Adams' claim comes after former Conservative Prime Minister John Major voiced his serious reservations about a deal between the Tories and the DUP to prop up the Conservative government.
Mrs May stressed that Brexit would happen and the timetable remains on course.
"We want the European Union to continue to remain strong and we want to continue to cooperate".
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