The four main opposition parties have united in a call for MSPs to be allowed to choose the next chairperson of the Scottish Police Authority (SPA).
Andrew Flanagan resigned from the role in June after being heavily criticised by two Holyrood committees.
The Scottish government is due to interview candidates to replace Mr Flanagan next month.
But opposition parties want his successor to be appointed by the Scottish Parliament instead.
In a joint letter to the justice secretary, they argued that the SPA - which is supposed to hold Police Scotland to account - needs to have "greater transparency and public accountability".
The Police and Fire Reform Act, which created the single national police and fire services, gives responsibility for appointing the chair of the SPA to the Scottish government.
However, the letter suggests that a committee of MSPs should instead be tasked with carrying out the appointment process and then making a recommendation to parliament.
The Scottish Conservatives, Labour, Greens and Liberal Democrats do not believe new legislation would be needed in order for responsibility to be delegated to the Scottish Parliament - although the Scottish government disputes this.
The opposition parties said the process would be similar to one that already appoints the heads of public bodies such as Audit Scotland and the Children's Commissioner.
In their letter, they said the SPA had been "under significant pressure and faced serious criticism" for several months, and it was vital that the right person was chosen to chair the organisation.
The letter added: "We would all like to move on from the difficulties that have been identified with the SPA and Police Scotland since their inception.
"We all want to see the single police force succeed and ensure that the public, along with serving officers and staff, can have confidence in its leadership.
"It is important that the next chair of the SPA has the support of the Scottish Parliament and we would urge you to consider this proposal to improve the appointment process of this important public role."
'Change to legislation'
Responding to the letter, a spokesman for the Scottish government said: "It is a requirement of the Police and Fire Reform (Scotland) Act, which received cross party support, that Scottish Ministers appoint the chair of the SPA.
"Moving to a system where the chair is appointed by parliament instead would require a change to legislation."
The Scottish government says that appointments made by the Scottish Parliament generally have a role in scrutinising or overseeing the work of Ministers and the Scottish government - which is not the case with the SPA.
When he announced his resignation, Mr Flanagan - who is staying on until a successor is appointed - said he did not want to become a "distraction" to the new 10-year policing strategy, and that the "personalised" debate over the SPA had impacted on him and his family.
It followed Holyrood's public audit committee and the justice sub-committee on policing both criticising Mr Flanagan, with the former raising "very serious concerns" and the latter saying they did not have confidence in his leadership.
The police watchdog is also investigating governance at the SPA after a board member quit amid a row over meetings being held behind closed doors and Mr Flanagan's failure to circulate critical correspondence.
Last month, SPA chief executive John Foley announced he would be retiring in October.