The Welsh Local Government Association (WLGA) believes education and lifelong learning minister, Jane Davidson, wants all councils to hit Assembly spending guidelines (standard spending assessments), published last week.
Although some councils have fallen short of their education SSAs, overall spending among the 22 councils was pound;21 million above the SSA in 2004-5.
WLGA director Steve Thomas told association members last week: "The minister has come up with the idea of insisting that authorities which don't spend up to their SSAs do so. But this is something which we have consistently opposed."
John Davies, the association's education spokesman, said the minister was under political pressure to seek assurances that the WLGA would encourage some local education authorities to spend more on education.
He said: "She wants an informal ringfencing. But many schools and authorities are happy with the current position and it is the teaching unions which are putting on the pressure.
"The minister says she does not want to go down the route of compelling authorities in this matter but we understand the political pressure she is under. We are spending a total of pound;21m in excess of the SSA."
He believes local authorities should be allowed to choose how they allocate their budgets.
Ms Davidson has encouraged schools to use the SSA figures in discussions with councils on education spending in local budget forums, which will start meeting in the new year.
But an Assembly government spokeswoman said: "There is no change to the policy regarding funding in that decisions rest with local authorities on the budgets for individual services. Our aim is to increase transparency by publishing indicative service figures within each local authority's SSAs.
"Local authorities are accountable at the local level and that remains the case. Publication of the figures mean they can no longer hide the information as it will be available when they set their budgets."
A WLGA spokesman said that if the Assembly government forced local authorities to comply with the SSA, it would mean cutbacks in other council services.
He added: "Some local authorities might be underperforming on education but we maintain it is all about local choices."
Teacher unions have long complained about the funding fog surrounding how much cash allocated by the Assembly actually finds its way into schools via LEAs.