Federal government payments to private schools would be determined by the income tax paid by parents at that school under a new funding model set to disadvantage some elite institutions but reward others.

The National School Resourcing Board will recommend using powerful data-matching tools to link parents' tax returns with their children's school enrolment, according to sources familiar with briefings delivered to school sectors on Wednesday.

The shake-up would have flow-on effects on the fees paid by parents at private schools of all stripes.

Funding shake-up: Loreto Mandeville Hall, an independent Catholic girls' school in Melbourne's Toorak. Credit:Cathryn Tremain

The overhaul would deliver a win for the Catholic sector, which believes the status quo is unfair, and potentially patch the fractious relationship it has had with Education Minister Simon Birmingham.