The way Catholic education authorities distribute taxpayer money for schools is under scrutiny as the federal government is on the verge of overhauling school funding arrangements.
Greens education spokeswoman Sarah Hanson-Young asked the Australian National Audit Office to look into the current and historical funding practices of Catholic authorities amid reports they were shifting money from poorer schools to better-off ones.
Auditor-General Grant Hehir replied to her on Thursday that his office was already examining the impact of school funding and wouldn't start a separate investigation into the Catholics alone.
"In the context of this audit the ANAO will consider, among a range of issues, transparency and accountability measures related to the provision of funding for schools by the Australian government," he wrote.
His reply comes as the Senate debates the government's new school funding deal, which will include a year's delay to some arrangements in a bid to allay Catholic - and some government backbencher - concerns.
Senator Hanson-Young says the revelation is extraordinary, given the government is preparing a special deal for Catholic schools.
"Reports that the Catholic education commission have been fiddling the books, funnelling money meant for poorer schools to overfunded wealthy schools, are alarming and I welcome the auditor-general's investigation," she told AAP.
"We need more transparency in schools funding and that is truer within the Catholic education sector than anywhere else."
As part of the funding package, the government has agreed to set up an independent National School Resourcing Board and the Greens are trying to give it powers to name and shame school authorities that don't distribute funding according to true need.
The audit is expected to report after August.