A DUP source told the Press Association that talks with Mrs May’s Conservatives “haven’t proceeded in a way that the DUP would have expected” and cautioned that the party “can’t be taken for granted”.
The development came just a day ahead of the Queen’s Speech, and threatens to leave Mrs May uncertain of her ability to secure a Commons majority for her Government’s legislative programme for the coming two years.
But the source said agreement before Wednesday’s State Opening of Parliament could not entirely be ruled out if there was movement in the talks between the parties.
The DUP is urging the Government to give “greater focus” to the negotiations.
Mrs May was forced to seek support from other parties after the snap election on June 8 left her nine MPs short of an overall majority in the House of Commons.
Speaking outside Downing Street the day after the poll, the PM said that she would “continue to work with our friends and allies in the Democratic Unionist Party” to ensure she was able to command a majority to get her legislation through.
But the Conservatives were forced to row back on a premature announcement that agreement had been reached on a “confidence and supply” arrangement, and talks have now dragged on for 11 days without reaching a conclusion.
A Number 10 spokesman would say only that talks were “ongoing”.
It is thought that the DUP is asking for more investment for Northern Ireland as part of the price of its support, and the party also wants the retention of the triple lock guarantee on pensions and winter fuel allowances for older people.
Arlene Foster’s party backs Brexit, but wants to avoid any disruption to movements across the border with the Irish Republic.
Mrs May has rejected claims that a deal with the DUP would undermine the Government’s ability to act as an honest broker in talks on the restoration of devolved institutions and power-sharing in Northern Ireland.
A confidence and supply arrangement would fall short of a full coalition.
The DUP would remain outside Government but would ensure its survival by guaranteeing to vote with it on financial measures and no-confidence votes.
Liberal Democrat Brexit spokesman Tom Brake said: “After one week of talks, we are no closer to finding out what the DUP have asked for and what concessions are being made.
“It’s time for the Conservatives to come clean and tell us: Is no deal better than a bad deal?
“Theresa May has no mandate for the direction she is taking the country.
“This is the first time in decades that a Prime Minister will propose a Queen’s Speech without a Commons majority.
“Her failure to reach a deal in time with the DUP doesn’t bode well for the tough Brexit talks ahead.”