Stephen House, chief constable of national force Police Scotland, and Vic Emery, head of the Scottish Police Authority (SPA) overseeing body, are due to give evidence to Holyrood's justice committee on Tuesday, amid a row over who will control the force's purse strings and other key backroom functions.
It came as the Association of Scottish Police Superintendents (Asps) – which supports Mr House – demanded urgent clarity, four months before the force is due to take over the running of policing north of the Border.
Mr House and Mr Emery have clashed over who will control force finances, human resources, the press office and other corporate services.
Mr Emery, an ex-boss of BAE Systems' shipbuilding arm and adviser to Edinburgh's ill-fated trams project, told MSPs this month bringing the functions under the control of the SPA would let the force "concentrate their focus on policing".
Mr House's supporters believe the chief constable must have full control of the force to safeguard its independence from the Government, which appoints and pays the SPA chairman and its 12 board members.
Labour MSP Graeme Pearson, a former senior police officer who headed the Scottish Crime and Drug Enforcement Agency, said: "The committee is inviting the various parties to rehearse their views and wants to question them on what each thinks they will be doing. My hope is that they will resolve their differences before the committee has a chance to meet.
"But if not, we may at least be able to clarify the differences between the various players and encourage the cabinet secretary to get off his backside and sort this."
Mr Pearson said the priority should be to protect the new force's operational independence from ministers.
He added: "The Government appoints the convener of the police authority and pays the members. If the authority is given control over the police budget, it places the Government in a very strong position to influence and control the chief constable.
"That's why we need to create an operational space to ensure the chief does the right thing, not the Government thing."
Mr House and Mr Emery gave conflicting accounts of the new police service of Scotland in presentations to an international policing conference in Edinburgh on Thursday.
One observer told The Herald they were "describing different police forces".
The new force has been unable to place formal job adverts for such key positions as heads of finance, corporate services, public information and human resources, because they are unable to say to whom they would report.
Chief Superintendent David O'Connor, president of Asps, said: "April 2013 fast approaches and we all need clarity over who runs the Police Service of Scotland: is it the chief constable or the police authority?
"The Scottish public trust the police and have confidence in delivering the police services they need and want. Policing in Scotland is not broken – what is the new SPA trying to fix?"
The SPA was set up to maintain and monitor the new force, holding the chief constable to account. Critics of Mr Emery say the body could not act as a watchdog if it was actively involved in running key backroom functions.
A Scottish Government spokeswoman said: "The police service of Scotland and the SPA will work closely together to ensure communities across Scotland continue to enjoy excellent policing.
"The legislation clearly sets out the responsibilities of the SPA and the Police Service of Scotland. The Chief Constable and the SPA will decide – in close dialogue with one another – how best to fulfil their respective responsibilities under the Act."