The two parties have said they will not nominate candidates themselves
The DUP and Sinn Fein have signalled they are moving towards a deal on devolving policing and justice powers from Westminster to the NI Assembly.
The parties have agreed there will be a single department of justice with a minister needing cross-community support to be elected.
The two parties have said they will not nominate candidates themselves.
But Alliance, the party most likely to supply a minister, has said it is not interested in taking on the post.
Transferring policing and justice has been one of the most contentious issues since devolution was restored to Northern Ireland.
The failure of Sinn Fein and DUP to agree on the issue has been a key factor in what some have described as a deadlock at Stormont.
However, the parties have written a letter to the Assembly Executive Review committee outlining common areas of agreement.
But there is still no agreement on when transfer of powers would take place.
The DUP's Jeffrey Donaldson said: "No decision has been made on timing of devolution and other areas such as financing are still to be worked through.
"We continue to work on the basis that sufficient community confidence is required before devolution can take place."
Sinn Fein's Gerry Kelly said the transfer should have happened in May, under the terms of the 2006 St Andrews Agreement.
"Sinn Fein want to see it happen in the short time ahead," he said.
"We have agreed with the DUP that powers would be transferred to a single department, with a single minister elected by cross community support and that initially neither ourselves nor the DUP would take on that ministry. This is a significant development."
The Alliance Party, widely touted as a possible compromise to fill the ministry, has said it will not take the post.
"This executive is incompetent, it's time they got with doing the job that they were set up to do," party leader David Ford said.
"It's a very definite and a very emphatic no."
Meanwhile, the SDLP has said it would "pursue its democratic entitlement" to hold the justice post.
"As the party which delivered the new beginning to policing, we are best qualified to take on the task of a devolved justice ministry.
"For the SDLP, this is natural territory," the party's Alban Maginness said.
Ulster Unionist leader Sir Reg Empey said the Alliance Party was right to reject the post.
"They were effectively being ambushed with the DUP and Sinn Fein trying to gerrymander the system," he said.
"This would've meant leapfrogging the SDLP, which was the party next in line for the role.
"That is because Sinn Fein can't tolerate the idea of the SDLP being in charge."
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