David Whitehouse and Paul Clark had been appointed joint administrators of Rangers in 2012, but were arrested in 2014 regarding their involvement with the administration.
The pair were awarded more than £20 million after charges brought against them were dropped or dismissed.
After they were cleared, they launched a civil action against the Crown Office and Police Scotland with the current Lord Advocate, James Wolffe QC, admitting liability last year.
Last month, Mr Wolffe told the Scottish Parliament a judge-led inquiry would be held, and has the backing of Police Scotland Chief Constable, Iain Livingstone.
But an online hearing at the Court of Session was held on Monday to discuss documents which Roddy Dunlop QC, for Mr Whitehouse, described as “substantial and which took an awful lot of time and money to recover”.
He confirmed Mr Whitehouse wants to use the documents “in order to effectively make a complaint to the relevant authorities” and that he will “co-operate with any investigation which may ensue”.
The Dean of Faculty told Lord Tyre the issue was of “real concern and worthy of investigation”, also questioning “how appropriate it is for the Lord Advocate to mark his own homework”.
Mr Dunlop added: “We have an unprecedented situation where it has been admitted [Whitehouse and Clark] were prosecuted maliciously and without probable cause.
“Mr Whitehouse has a justifiable concern that it’s already been said in open court on behalf of the Lord Advocate last time around that it’s already been determined there’s no evidence of criminality.
“Mr Whitehouse is entitled to raise the query, ‘How can that be?’
“Misconduct in public office is a crime under the common law in Scotland, and one might have thought a malicious prosecution would at least qualify as misconduct in public office.
“Mr Whitehouse gains no private interest by bringing this application, by bringing this complaint, by asking for an investigation. This is a clear case of an over-riding public interest – how did this happen?
“Mr Whitehouse should be able to take the documents, pass them to the police, and say, ‘please look at that and investigate’.”
In his reply, Gerry Moynihan, representing the Lord Advocate, said: “The Lord Advocate has said in the Scottish Parliament that in due course an inquiry should take place, such an inquiry cannot take place until all other legal proceedings have been concluded.
“The nature and form of the inquiry are not yet determined. My understanding is it has not yet been determined that will be a public inquiry under the Act as opposed to in private.
“The terms of reference have not yet been determined and it’s accordingly difficult to determine what documentation is necessary in that context.
“If Mr Whitehouse makes any complaints of a disciplinary or criminal nature, those will require to be investigated.
“The priority is to conclude the civil actions, properly consider any complaint, and only after that would the judicial inquiry arise.”
Lord Tyre’s written judgment on the documents is expected to be published later this week.