It follows the refusal of Social Development Minister Mervyn Storey to hand over the document without any of it being blanked out.
The Social Development Committee met in closed session to discuss the impasse on Thursday.
It is believed they decided third party mediation may provide a way forward.
The plan would involve the minister agreeing to hand the report to a judge appointed by the Lord Chief Justice.
The judge would then decide whether or not the committee should be given the document in un-redacted form.
It is understood the committee agreed to its chairman, Alex Maskey of Sinn FÃ©in, meeting Mr Storey to propose the idea.
However, no formal vote on the plan was taken as Mr Maskey did not want the committee to "divide."
So far there has been no official comment from the committee, but it is believed the idea was proposed by the TUV leader Jim Allister.
Last week, the minister gave the committee a copy of the report into the conduct of the adviser, Stephen Brimstone.
It was carried out by civil servants, but its findings had remained secret for 18 months amid allegations it had been "buried".
The report recommended a formal disciplinary investigation into Mr Brimstone's behaviour.
But a series of other conclusions and recommendations were concealed.
One source said it would be up to the judge to decide the "relevancy" of the parts of the report that have up to now been hidden.
The committee has been investigating allegations of political interference in the Housing Executive.
They were raised in a BBC Spotlight programme in 2013.
It is claimed Mr Brimstone ordered a DUP councillor to change the way she intended to vote at a Housing Executive Board meeting.
The BBC has learned that Mr Storey sent a letter to Mr Maskey on Wednesday afternoon.
It is understood the minister has legal advice telling him he does not have to comply any further with the committee's demand.
A High Court judge may be called in to decide if a Stormont committee should be given a full copy of a report into the conduct of a DUP special adviser.