A senior Democratic Unionist has said it is "much too early" to talk of a formal agreement with a minority Conservative government.
Sir Jeffrey Donaldson's comments come amid mounting speculation that the two parties will come to some form of understanding that will enable the Tories to form an administration.
The pro-Brexit DUP, which returned 10 MPs to Westminster, has found itself kingmaker in the hung Parliament.
Ahead of the election, Northern Ireland's largest party made clear its preference was for a Tory rather than Labour government.
In a speech, cancelled in the wake of the Manchester terror attack, Ms Foster planned to describe Jeremy Corbyn as "beyond the political pale" because of his past support for Irish republicans.
She attacked the Labour leader's credibility, including warning that it was hard to take him seriously because of his meetings with political representatives of the IRA at the height of the Troubles.
Mrs Foster was due to set out her stall at a meeting of the pro-Brexit Bruges Group in Mayfair on May 22 but pulled the speech after Ariana Grande's concert in Manchester was targeted by a suicide bomber.
Prior to the 2015 election, with the pollsters predicting a hung parliament, the DUP ruled out a potential formal coalition with the Conservatives, instead indicating its support would be offered in a confidence and supply arrangement from the opposition benches.
The DUP and Sinn Fein dealt a series of devastating blows to their rivals in Northern Ireland to emerge from the General Election stronger than ever.
The two main parties advanced as the Ulster Unionists and SDLP were wiped off the Westminster map.
Sinn Fein's seven MPs are not part of calculations to form a government because the republican party refuse to take their seats in Westminster.
Sinn Fein president Gerry Adams hailed what he described as an historic result for his party.
"Sinn Fein respects the mandate we have received and our electorate who voted in such huge numbers," he said.
"Nationalists and republicans have turned their back on Westminster and accept that that centre of political gravity is now on the island of Ireland.
"The Taoiseach and DUP need to focus on restoring the political institutions.
"Theresa May sought a mandate for Brexit, austerity and the erosion of human rights. She got her comeuppance.
"The Irish government needs to seize the initiative to secure designated special status for the North as part of the Brexit negotiations."
Returned DUP MP for East Belfast Gavin Robinson said any deal would be on the basis of a confidence and supply arrangement.
"We have essentially got the result we were campaigning for two years ago," he said.
"It didn't materialise then but we campaigned on the basis of a hung parliament two years ago.
"I think that puts us in a fantastic position to deliver for Northern Ireland."