The PSNI has told Belfast City Council it plans to start charging a fee for providing support during Eleventh Night bonfire clear-up operations.
It is understood councillors were told of the development by council officials last week.
Belfast City Council said materials were gathered on 22 of its sites this year.
Read More: CCTV cameras at controversial east Belfast bonfire site disabled
What are eleventh night bonfires in Northern Ireland?
In recent weeks, chief constable Simon Byrne has raised concerns over cuts to the PSNI, which is facing a £107 million shortfall following a budget set by Secretary of State Chris Heaton-Harris earlier this year.
There was controversy last month after it emerged that violent, sectarian and Nazi images were on display at a bonfire builders' hut at a council-owned site at Lisnasharragh leisure centre.
The images included a flag depicting a masked man holding a rocket along with the words 'Clonduff Rocket Team' and a Swastika etched into a makeshift table.
The letters KAT, 'Kill All Taigs' were also scrawled into a sofa in the hut.
Election posters belonging to Alliance councillor Michael Long, a tricolour and a Clonduff Roacket Team flag were placed on the bonfire before it was set alight earlier this week.
SDLP councillor and group leader Séamas de Faoite voiced concern over the proposed PSNI approach.
“Belfast’s ratepayers should be able to have confidence that the PSNI will support lawful efforts by Belfast City Council or other public agencies to remove dangerous or damaging bonfires from their land," he said.
“The city cannot afford to go down a path where the PSNI and others refuse to live up to their obligations, and lawlessness prevails as a result.
"The only winners in that scenario are those who intimidate local residents, damage public property and promulgate hatred and sectarianism."
He suggested that the PSNI position is wrong.
“The PSNI should absolutely not be seeking to pass on the costs of policing these scenarios to any council or any other public body," he said.
"Issues around policing budgets must be addressed by a restored and reformed Stormont, rather than become an unreasonable burden for councils.”
Green Party group leader Brian Smyth also expressed concern.
“We need statutory bodies to be working together to address problematic issues within our communities," he said.
"The PSNI have a duty to protect life and property and simply can't throw policing costs back to councils.
"If a bonfire site anywhere in Northern Ireland is assessed to pose a risk to either, then we need the police to intervene without arguments around costs being at the fore."
Mr Smyth said he has concerns about the message being sent out.
“This could send a dangerous signal to those who engage in criminal behaviour and intimate communities," he said.
"We know that their budget is under considerable pressure, just like many other areas in the public sector after 13 years of relentless Tory austerity.
"Yet we can't have the scenario where a council is left to deal with the possibility of criminal behaviour without worrying about cost implications it may have from the police.”
A PSNI spokeswoman said: "Police engaged with the Belfast City Council, but no formal requests were received to support a removal operation of Clonduff bonfire."
A spokeswoman for Belfast City Council, earlier in the week, said its "approach to managing bonfires is led by elected members".
Said added that council was "aware of bonfire materials being gathered at a number of sites across the city, including on land which it owns" and that a "member-led decision-making process has been agreed to consider issues and make decisions on a site-by-site basis".
“We continue to engage with elected members and community representatives to minimise any potential negative impact of bonfires and associated anti-social behaviour on local residents, businesses, customers and property,” the spokeswoman added.
