The event had to be delayed as Theresa May didn't gain a majority in the general election, forcing the Conservatives into talks with the Democratic Unionist Party, so that they can form a viable government.
The Queen's Speech, which outlines the Government's policies for the parliamentary session, will take place on Wednesday 21 June.
The source said: "Talks are progressing well and there's agreement on the principles of the Queen's speech".
He explained that the two parties are both committed to delivering Brexit, fighting terrorism, preserving the United Kingdom and boosting economic prosperity, giving a clue as to what will be included.
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The big games continue with Liverpool hosting Arsenal the following weekend, before Jurgen Klopp's men travel to Manchester City. This match will be rescheduled, however, with the Rugby League Challenge Cup final taking place on the same day.
The date of the Queen's Speech was not relevant to the talks, Dodds was quoted as saying.
Moving the speech will disturb the Queen's attendance at this year's Royal Ascot.
But Tories were unwilling to say what meetings are expected over the coming days.
But she has also forced a change in the Queen's diary as the Monarch had been due to attend Royal Ascot horse races on June 21.
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But with the address due to start at 11.30am she is likely to have ample time to take part in her traditional arrival ceremony, a carriage procession usually held in the early afternoon.
The Sinn Féin leader, Gerry Adams, said he believed the deal would be in breach of the Good Friday agreement because it would undermine the government's role as a neutral convener.
Mrs Long added: "We have to be practical about these things".
Colum Eastwood, the leader of the nationalist SDLP, said the government needed to "prove to the rest of us that they are not under the thumb of the DUP".
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He punched the third back into the fairway but needed two more to get on the green and two to get down for his second seven. However, he was still well outside the top 100 at five over, with only the top 60 and ties making the weekend.
"I think one of the most shameful aspects of the whole Brexit process from the beginning to now has been the disregard shown by many for that peace process".
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