Martin McGuinness: "I have to say I'm pleased with the outcome"
The first and deputy first minister are to brief their parties following further talks on the devolution of policing and justice in Downing Street.
The discussions went on until late in the night and afterwards Sinn Fein's Martin McGuinness said "massive progress" had been made.
He said all sides were "on the cusp of agreement" on a financial package to fund the transfer of the powers.
The DUP's Peter Robinson said he would respond after speaking to his party.
The two parties have been arguing over when the transfer of powers to Stormont should take place.
Thursday night's discussions ended at about midnight after more than four hours.
Peter Robinson: "We are not going to pushed or bullied"
BBC Ireland correspondent Mark Simpson said it was too early to say a deal had been done, but government sources had indicated they were cautiously optimistic about the outcome.
Prime Minister Gordon Brown has spent all week trying to find agreement over the questions of finance and timing.
Our correspondent said the financial problem appeared close to resolution, but the timing of the transfer was still unclear.
Mr McGuinness, Northern Ireland's deputy first minister, wants it to happen immediately.
He told reporters outside Downing Street that he was "pleased with the outcome" of the talks.
We will want to be sure that the issues that we have discussed are interpreted and expressed in the communication in the way that we would expect
Peter Robinson First Minister
He said: "We've effectively concluded our discussions on the funding issues in relation to the transfer of power in policing and justice.
"So I have to say, I think a good night's work has been done."
Mr Brown is to send details of the package to Northern Ireland political parties on Monday.
First Minister Mr Robinson said he would make his position clear once he had consulted his party colleagues.
He insisted that his party would not be "pushed or bullied or bribed".
Mr Robinson added: "The prime minister understands the issues. He is going to put together his proposal on paper.
"I've been in many sets of negotiations and we will want to be sure that the issues that we have discussed are interpreted and expressed in the communication in the way that we would expect, and then colleagues are going to have to make a judgement based on the proposition."
Thursday night's meeting was the third between the prime minister and the first and deputy first ministers this week.
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