Martin McGuinness and Peter Robinson have been holding talks in New York
First Minister Peter Robinson has said he will promote to unionists the devolution of justice powers if the financial aspects can be perfected.
The DUP leader was speaking after discussions in New York with the US Secretary of State Hillary Clinton.
Deputy First Minister Martin McGuinness said the length of talks he and Mr Robinson are having with Gordon Brown was not a cause for concern.
He said he hoped the financial details could be resolved by next week.
The two men are due to meet the prime minister again next week at the Labour Party conference in Brighton.
Mr McGuinness said: "There are a number of agencies we are dealing with in terms of policing and the legal system.
"We have presented him with figures which he is examining and I think we are close to agreement."
BBC Northern Ireland political editor Mark Devenport said the attitude of the DUP was crucial.
Mr Robinson said he had a "selling job" ahead of him once financing was agreed.
"I believe that the structures that we've put in place are sufficient to command that confidence and I want to do the same with the financial arrangements," he said.
"When we do that, we have a selling job to the community as a whole.
"We have to be sure that we're bringing people with us. It will be a selling job - I don't intend to be neutral in that."
On Wednesday night, Ulster Unionist leader Sir Reg Empey warned that there should be no more secret deals over policing and justice and every party should be informed of the details.
Speaking after the Clinton Global Initiative conference on Northern Ireland, Sir Reg also called for greater openness about the general financial health of the Stormont Executive.