The Turnbull government is aiming to use the successful passage of its childcare reforms, which redistribute subsidies from wealthy to low-income families, as a springboard to overhaul the way schools are funded.
The government is examining trimming funding to "over-funded" private schools and redistributing money to needy public and non-government schools as part of the new funding model.
Education Minister Simon Birmingham will shift his attention to schools after the Senate passed the government's $1.6 billion childcare package on Thursday night.
Fairfax Media understands cabinet has discussed school funding repeatedly over recent months and is close to finalising the government's position.
The government is expected to sell its policy, which will be less generous than Labor's, on the grounds it creates fairness between states and school sectors.
Changing indexation rates so schools transition more quickly to their appropriate resourcing standard would require Senate approval.
Around 150 private schools receive excess government funding and it will take decades for some to arrive at their appropriate standard under the current formula.
But a final deal on school funding is likely to be delayed until the middle of the year, leaving little time to implement a new model before it takes effect next year.
Senator Birmingham has consistently said that new four-year funding arrangements would be resolved at an April COAG meeting between the Prime Minister and state and territory leaders.
But the COAG meeting has been delayed until after the May budget and is not expected to take place in June. It is understood the April meeting was cancelled at the request of two state premiers who could not attend.
Senator Birmingham will seek to advance the issue when he meets with his state counterparts on April 7.
The independent and Catholic school sectors had already said they were "increasingly alarmed" at the lack of detail from Canberra and that the uncertainty was disrupting principals' planning for next year.
Labor schools spokeswoman Tanya Plibersek this week shifted her rhetoric by saying Labor was "very happy to talk about bringing overfunded schools down to a fairer rate of funding more quickly if the Government actually proposes that".
"There's no concrete proposal on the table from the Government to reduce funding for overfunded schools," Ms Plibersek said.
"The only concrete proposal from the Government is to reduce all funding to all schools, right across Australia."
Ms Plibersek previously said there was no "compelling" case to reduce funding to overfunded private schools as only a small number of schools receive excess funding.
Prime Minister Malcolm Turnbull on Friday said the government had achieved an "outstanding reform" by passing its childcare package.
"It will benefit around a million families," he said. "It's targeted to those who work the longest hours but earn the least."
Childcare groups said they were bitterly disappointed the Senate crossbench did not force the government to raise the minimum subsidised hours of childcare from 12 to 15 hours a week.
"This leaves up to 100,000 children from low-income families without the support they need," Goodstart Early Learning spokesman John Cherry said.
"While many working families will be better off as a result of the childcare reforms it is disappointing that modest changes which would have protected children from very-low-income families have been ignored."
