He said he also had concerns about the Independent Police Complaints Commission, which is having to recruit new investigators to cope with the scale of its investigation into the Hillsborough police cover-up.
He added: "The temptation will be to recruit ex-police officers. I query whether that is the right thing to do."
He said lawyers or academic historians could provide the expertise needed.
"It needs a little bit of imagination."
The Attorney General’s office has already told campaigners he hopes to make an application to the high court to quash the inquest verdicts of "accidental death".
Mr Abrahamson said families wanted one overall person to be in charge of the investigations, but he questioned whether the Director of Public Prosecutions was the right person.
He said: "We want someone in a hands-on supervising role.
"The DPP can’t do that unless he resigns his current job because he is so busy with other things.
"We think it should be someone of at least national or international stature with experience of supervising complex events."
He said it could be an individual with experience of monitoring elections or investigating war crimes, for example.
He said HJC are clear that the inquests should be presided over by the chief coroner or a high court judge.
"I will be arguing that one of the functions should be to look at the cover up, in order to prevent an incident of this type happening again."
The issue of compensation is also being looked into.
"We can certainly argue that the settlements reached were based on errors of fact.
"The 3.15 cut-off was wrong, there was a police cover-up, and people suffered more than was previously thought.
"Also there is the issue of survivors and post-traumatic stress which was expected to be resolved.
"But because they never got the truth it has been at the forefront of their minds of 20 years longer than it ought to have been."
He said because of time limitations already having been passed, applications to the courts for civil cases would have to be made relatively quickly and possibly before criminal cases had been heard.
"We could start those proceedings and then ask for them to be stayed until the outcome of criminal cases.
Mr Abrahamson continued that it would be sensible for the government to establish a fund for claims like it did in the immediate aftermath of the disaster.
And he said his team needed to get to investigate what happened to the original fund.