Lawyers for the six, who include match commander David Duckenfield, are claiming that prosecution would be an 'abuse of process'.
A hearing, before judge Sir Peter Openshaw, sitting as a judge of the Queen's Bench Division of the High Court, began at Preston Crown Court today and is expected to last for up to 10 days.
At the same time, prosecutors are also applying for legal clearance to charge Duckenfield, now 73, with 95 counts of gross negligence manslaughter in relation to the 1989 disaster.
Currently, they are prevented from doing so by a stay on further prosecution. This was awarded to Duckenfield in 2000 after a private prosecution was brought by the families of those who lost relatives during the FA Cup semi-final between Liverpool and Nottingham Forest at Sheffield Wednesday's ground.
Duckenfield is due to go on trial in September alongside Graham Henry Mackrell, 68, who was Sheffield Wednesday Football Club's company secretary and safety officer at the time, and faces two charges of contravening a condition of a safety certificate and one health and safety offence.
Former Chief Constable of West Yorkshire Police and Merseyside Police, Sir Norman Bettison, who was a Chief Inspector with South Yorkshire Police in 1989, is due to go on trial in May 2019, charged with four counts of misconduct in a public office.
Peter Metcalf, 68, a retired solicitor who acted for South Yorkshire Police during the earlier Taylor Inquiry and the first inquests, has been charged with doing acts with intent to pervert the course of justice.
He is due to stand trial in January 2019 alongside two retired police officers, former Chief Superintendent Donald Denton, 80, and former Detective Chief Inspector Alan Foster, 71, who are also charged with doing acts with intent to pervert the course of justice.
Ninety-six Liverpool fans were crushed to death in pens in the Leppings Lane end of Hillsborough Stadium as the FA Cup semi-final began.
Under the law at the time, there can be no prosecution for the death of the 96th victim, Tony Bland, as he died more than a year and a day after the injuries were caused.
Press restrictions on reporting the hearing in full have been imposed by Sir Peter until further notice.