Ninety-six Liverpool supporters died in a crush at Sheffield Wednesday's Hillsborough stadium on 15 April 1989 where their team was playing an FA Cup semi-final against Nottingham Forest.
The 20th anniversary of the tragedy was marked with memorial services in all three cities last Wednesday.
The victims' families have been fighting for further inquiries into the deaths as they dispute the findings of the single inquest into all 96 deaths, which ruled the victims were all dead, or brain dead, by 3.15pm. A verdict of accidental death was subsequently recorded.
Official documents are usually only released after 30 years, but Home Secretary Jacqui Smith has discussed waiving the rule in this instance with South Yorkshire's chief constable Meredydd Hughes.
Smith said: "The Government is committed to helping those who lost loved ones in the Hillsborough tragedy.
"That is why I will be working with colleagues in the Ministry of Justice, the Department for Culture, Media and Sport, and the Attorney General's Office to put out any information that exists that could shed light on the disaster and its aftermath in the public domain as soon as possible."
Trevor Hicks, of the Hillsborough Families Support Group, said on Sunday:
"We have heard that a request has been made and we are expecting confirmation this week.
"I am pleased, it's better late than never.
"This will enable us to see the full picture of events in a way that we have been denied for 20 years.
"It is vital that these files are released in full and not sanitised in any way.
"The families would also like a short period to view the documents before they are made public.
"Some of them are bound to contain information about the manner in which our loved ones died, their medical conditions and so on.
"I think it's best if we learn of that ourselves and not through other parties."
The families say they are particularly keen to see the minutes of a meeting between then Prime Minister Margaret Thatcher and senior South Yorkshire police officers which they say took place on the Sunday morning after the disaster.
Mr Hicks said: "We believe that a decision was made at that meeting that the police would not be blamed for what happened.
"We would like to see the minutes of the meeting, to know what the Prime Minister was told and what decisions were taken about the handling of any inquiries."
Mr Hicks added: "The claim that all the 96 were dead at 3.15pm has never been accepted.
"We would also like to know who gave permission for certain police officers to retire on the grounds of ill health before they could be prosecuted for negligence of duty."