An agreement for the Director of Public Prosecutions to lead all Hillsborough investigations can be expected when the Home Secretary meets with the Hillsborough Families Group.
The Home Secretary Theresa May will meet with the Hillsborough Families Group on Thursday afternoon, Channel 4 News' Political Correspondent Michael Crick has said.
Lord Falconer has said David Cameron has made a "huge difference" to the Hillsborough families' pursuit of justice.
"It is the failure of all previous governments that went before until the current Prime Minister responded so well in relation to the report that has made the difference," he said.
"So now you have a Government, led by a Prime Minister, saying, 'This is a huge injustice, let's sort it out' - and that makes a real difference."
Lord Falconer added that the Government's follow-up to that support is "absolutely critical".
Lord Falconer has said it is "absolutely vital" that the new investigations into the Hillsborough disaster are carried out "as quickly as possible".
"It doesn't need to take years," he told the Home Affairs Select Committee. "All the information is there."
Lord Falconer, an adviser to the Hillsborough victims' families, has told the Home Affairs Select Committee that the Director of Public Prosecutions believes the two probes into the conduct of officers at Hillsborough should be united as a single investigation.
He said the families endorsed the director, Keir Starmer QC, as the person to "coordinate and drive forward" a combined investigation, with the DPP effectively leading the IPCC probe.
Sheila Coleman, a spokeswoman for the Hillsborough Justice Campaign, has said the families and survivors "seek clarity" into the latest investigations into the conduct of serving and retired officers during the disaster.
She said they want assurances that no-one else involved in previous investigations into Hillsborough is involved in the current investigations launched by the Independent Police Complaints Commission and the Director of Public Prosecutions.
Mrs Coleman also said she was "heartened" to hear the Chief Constable of South Yorkshire Police did not want its force to play any part in the investigation into the conduct of its officers during Hillsborough.
South Yorkshire Police's Chief Constable David Crompton has told ITV News' UK Editor Lucy Manning that his force will not oppose a request for new inquests into the Hillsborough disaster.
But he stopped short of saying his officers were likely to appear in court over their role in the tragedy and its aftermath.
On his way into the Commons, South Yorkshire Police's Chief Constable David Crompton said he welcomed the decision to review the inquests on Hillsborough, saying it was the "right move."
Chief Constable Crompton has been called to the Home Affairs Select Committee to update it on his actions after the publication of the Hillsborough Independent Panel Report.
South Yorkshire Police will submit to the IPCC a list of its police officers who were at Hillsborough and are still serving in a week to two weeks, the force's Chief Constable has told MPs.
David Crompton said he believes the list will be around 100 officers, rather than 200 as has been suggested.
Margaret Aspinall and Trevor Hicks from the Hillsborough Family Support Group said they were "delighted" the Attorney General had announced he will apply to the High Court to quash the original inquest verdicts.
They said it was important that they had the same legal support afforded to the police officers, and they want the inquest to be held in Liverpool.