Handing over responsibility for policing and justice to an SDLP or Ulster Unionist Party minister is one of the models being considered to resolve the policing stand-off between the DUP and Sinn Féin, according to senior political sources.
As Friday's Assembly meeting - postponed because of the attack on Parliament Buildings by Michael Stone - reconvenes today, the focus turns to policing.
As well as concluding Friday's meeting, the Assembly is to hear a report on the security implications of Stone's attack.
It is likely now that armed PSNI officers will carry out security duties at Stormont to assist unarmed security guards.
Stone's early release licence under the Belfast Agreement has been revoked and he is now due to serve the remaining 18 years of the 30-year minimum sentence imposed on him for a 1988 attack at Milltown Cemetery, in which he killed three people.
The British and Irish governments are now satisfied that comments made by DUP leader Rev Ian Paisley inside and outside the Assembly chamber on Friday mean he is conditionally prepared to be First Minister.
The governments believe the process can now move to the next stage of the St Andrews Agreement, persuading Sinn Féin to call an ardfheis to endorse and support the PSNI and the rule of law.
However, the DUP and Sinn Féin remain deadlocked on this issue. Sinn Féin is demanding a date for the devolution of policing and justice to the Northern Executive while the DUP is insisting that no such commitment can be given.
North Belfast MP Nigel Dodds, in particular, has angered Sinn Féin by stating he could not see this devolution taking place within a "political lifetime".
Northern Secretary Peter Hain said yesterday that such remarks from Mr Dodds and other leading members of the DUP were unhelpful.
Equally, he said Sinn Féin must provide clarity by calling the ardfheis on policing, and this should take place before the election.
The governments are currently working to an expectation that the Sinn Féin ardfheis will be called before the end of January when the Assembly election campaign formally begins.
Sinn Féin Assembly member Francis Brolly caused surprise when he was reported on Friday in Swiss newspaper Le Temps as saying the ardfheis might not be called until the summer. Mr Brolly later issued a statement saying he had been misquoted and that responsibility for calling the ardfheis rested solely with the party leadership.
Some Sinn Féin and DUP sources have indicated that there is a possible way of breaking the deadlock over when policing and justice would be devolved to the Northern Executive.
"One of the models currently being considered is that rather than having a Sinn Féin or DUP minister in charge, the department could be run by a Ulster Unionist or SDLP minister, or that the department could be shared between UUP and SDLP ministers," said a senior source.
The governments now hope the Assembly programme for government committee, which also meets today, will begin discussing whether this or other models could break the deadlock.
