The Government's top lawyer believes there is a "good" case for setting aside the accidental death verdicts and holding new hearings into the deaths of the 96 Liverpool supporters killed during their FA Cup semi-final with Nottingham Forest in 1989.
The latest move follows a damning report into the tragedy revealed a cover-up which attempted to shift the blame on to the victims.
Mr Grieve is planning to appear in person at the High Court to argue that new evidence means fresh inquests should be held.
"I believe that the case for the High Court to quash the original inquests is a good one," he said.
"My application has now been lodged with the Court. It is my intention to appear to argue the case at the hearing that will take place in the High Court."
If the court does decide to quash the original inquests and order new ones be heard, it can only refer the cases back to the district in which they were originally heard.
In 95 of the cases that would see them being sent back to Sheffield or Doncaster, with the Attorney General understood to be ready to suggest the court return the cases to the latter.
The families of those fans who died at Hillsborough have made it clear they want the new inquests to be held in Liverpool but a spokesman for the Attorney General's office said the location will be "a matter for the coronial process".