South Yorkshire Police, the force in northern England at the centre of the scandal, said it was ready to refer the matter to the national watchdog that has powers to recommend prosecutions.
A damning report on Wednesday uncovered evidence that the police response to the worst sporting disaster in British history was flawed, 41 lives could have been saved and officers tried to deflect the blame on to fans.
Their families have fought a 23-year campaign to uncover the truth about what happened and disprove official smears that blamed the crush on drunken, ticketless fans forcing their way into the stadium.
"South Yorkshire Police is currently reviewing a wide variety of matters raised in the report...with a view to making a referral to the Independent Police Complaints Commission (IPCC)," the force said in a statement.
The report said that 164 police statements were amended, with 116 of those edited to paint the police in a better light. It said the police had no proper emergency plan and organised a campaign to conceal their failings.
The IPCC watchdog said the panel's report "raised extremely serious and troubling issues for the police".
"There is a huge amount of information...that needs to be analysed and digested," it said. "We are aware that South Yorkshire Police are also carrying out a detailed assessment of the report with a view to making a referral to the IPCC."
Relatives of the victims said the panel's report provided enough new evidence to begin criminal proceedings against police officers and to overturn the original inquest verdict of accidental death.
Trevor Hicks, who lost two daughters at Hillsborough, said there had been a "dirty tricks campaign to deflect the blame" and that those responsible should be prosecuted.
Deputy Prime Minister Nick Clegg told the BBC there appeared to be "evidence of serious criminal activity" and the "wheels of justice must now turn".
A spokesman for Prime Minister David Cameron, who offered a profound apology to the families on Wednesday, said any decision on criminal charges would be taken by state prosecutors.
Norman Bettison, who is chief constable of West Yorkshire Police and was a senior officer with South Yorkshire Police at the time of Hillsborough, said he had "absolutely nothing to hide".
"I never altered a statement nor asked for one to be altered," he said in a statement.
The Football Association (FA) apologised on Thursday and said the disaster should never have happened.
A former Conservative member of parliament named as one of the sources of the inaccurate media coverage that blamed drunken fans for the tragedy said on Thursday he was "deeply and sincerely sorry".
"It is now clear that the information I received from some police officers at the time was wholly inaccurate, misleading and plain wrong," Irvine Patnick said in a statement.