The officials will meet at the Convention of Scottish Local Authorities (Cosla) at the end of next month.
Highland Council's leader Jimmy Gray has confirmed he will raise the issue, seeking pan-Scotland support for Highland's call for a fundamental review of the Chief Constable's decision.
Sir Stephen House issued a standing firearms authority for 275 officers across Scotland, who must wear side-arms whenever they are on duty.
However, local concerns have been raised over the appearance of armed officers in inappropriate settings, from shops to a charity event.
One senior local government figure, who wishes to remain anonymous until the council leaders have had a chance to vote, told the Herald: "I would be absolutely gobsmacked if Jimmy Gray does not get support for this.
"I think every local politician from every party has serious concerns about this issue. It is a blanket solution to what used to be a matter for local political decision-making."
Mr Gray, a Labour councillor who was formerly the Provost of Inverness, said other council leaders had already brought up the matter with him.
He said: "They have been just as concerned as we have in the Highland Council at armed police officers becoming a permanent feature in the policing of Scotland.
"They are wondering where it came from and, like us, are completely unaware of any discussion of the issue. We are all wondering what has happened to policing with consent as the guiding principle."
Sir Stephen and the Scottish Government have insisted that it was "an operational decision" to issue the standing authority and therefore could not be subject to political interference.
But Mr Gray said he agreed with Professor Alan Miller, chair of the Scottish Human Rights Commission, who said this week that this was not simply an operational matter for the Chief Constable alone to decide.
Mr Gray said there was no legal definition of what the "operational independence" of the police means.
"It was a term which has been around since 1960s," he said. "It is for when a decision has to be taken about how police should react to a given situation there and then. It clearly does not refer to a decision to change the pattern of policing."
He continued: "If operational freedom means the Chief Constable can arm 10 officers in the Highlands, does it mean he can arm them all if he so chooses? Would that still be an operational matter?"
But in a letter to the Inverness Courier, retired senior police officer John Darcy, who was firearms tactical commander with Northern Constabulary from 2003 to 2013, had a different perspective.
He said there were many legally held firearms in an area like the Highlands. He said: "Though infrequent, there have been many occasions when an individual, legally in possession, has undergone a life-changing event, sometimes exacerbated by alcohol and drugs, and intimated they are about to harm themselves or others."
Meanwhile, those of a violent nature, again possibly influenced by drink or drugs, could be brandishing bladed weapons, often in a domestic setting, and an unarmed response would not be appropriate. Organised crime gangs had also long targeted the Highlands for the sale of drugs.
"The situations described are predominantly spontaneous and as such require an immediate armed response," he said. "It was often frustrating to have to deploy unarmed officers between the public and danger, while waiting for a response-trained team to be ... ready for deployment."