The move comes as new Education Department data shows the glacial speed at which schools are currently moving towards their appropriate funding level – a process Education Minister Simon Birmingham wants to speed up.

Fairfax Media understands Senator Birmingham's school funding proposals have been discussed in detail during cabinet meetings over recent months, but a final position to present to state governments and the Parliament has not been approved.

The government is aware of the fraught politics of school funding including the political power of the Catholic and private school sectors. Securing Senate support for any changes will also be difficult.

There are no plans to cut funding for private and Catholic schools in real terms but the government is examining how to pull back the generous annual funding increases locked into legislation by the Gillard government.

Echoing comments he made last year on the ABC's Q&A program, Senator Birmingham said last week that a fair funding deal "means having something that is consistently applied and yes, that means that if some schools under formulas that have been grandfathered for years and years are getting more than their fair share then we ought to have a look at an adjustment process".

"Equally, of course, there are schools, including in the non-government sector, who are getting less than what formulas would say their fair share is and ... they'll have an adjustment process."

New data from the Department of Education shows private schools are crawling towards their appropriate Schooling Resource Standard (SRS) under the Gillard government's Gonski legislation.

It would take many schools decades – and some up to a century – to reach their appropriate funding level under their current trajectory.

Exclusive Sydney girls school Loreto Kirribilli, for example, was funded at 283 per cent of its SRS in 2014 – a level projected to decrease to 276.76 per cent this year

Meanwhile Hawkesbury Independent School is projected to receive 84.2 per cent of its SRS this year, up from 79.8 per cent three years earlier.

Melbourne Grammar School is projected to receive 140.7 per cent of its SRS funding this year, slightly down from 143.7 per in 2014.

By contrast, Kingswood College in Box Hill is projected to receive 87.8 per cent of its SRS funding this year, up from 82.5 per cent three years earlier.

NSW public schools will be funded at 89 per cent of their SRS this year and Victorian public schools at 83 per cent.

Colette Colman, executive director of the Independent Schools Council of Australia, said: "The 16 per cent of independent schools that are receiving funding in excess of their SRS funding model entitlement are now in their fourth year of transitioning to the model.

"It is important to clarify that no independent school's public funding is currently 'grandfathered'.

"The vast majority of independent schools are in fact receiving less than their public funding entitlement and are transitioning upward."

The Grattan Institute has found the 150 private schools above their SRS are over-funded by $215 million a year – spending it describes as "wasteful and inefficient".

Fairfax Media understands Senator Birmingham is also examining special deals struck between Labor and the Catholic school sector. He also wants to tie federal funding to commitments from state governments so they will not reduce their own education budgets.

Labor education spokeswoman Tanya Plibersek has said Senator Birmingham's comments about inequities in school funding were "diversion tactics" to distract from the fact the government is not funding years five and six of Labor's Gonski agreements.

Over-funded schools*

NSW: most over-funded private schools 

Loreto Kirribilli 
Government funding to School Resourcing Standard: 277%
Annual government over-funding: $4.7 million

Monte Sant' Angelo Mercy College 
Government funding to School Resourcing Standard: 268%
Annual over-funding: $5.2 million

Mount St Benedict College
Government funding to School Resourcing Standard: 212%
Annual over-funding: $5.2 million

Brigidine College, St Ives
Government funding to School Resourcing Standard: 187%
Annual over-funding: $4 million

Northern Beaches Christian School, Terrey Hills
Government funding to School Resourcing Standard: 184%
Annual over-funding: $5.1 million

Victoria: most over-funded private schools 

Melbourne Grammar School
Government funding to School Resourcing Standard: 141%
Annual over-funding: $2.2 million

Lauriston Girls' School, Armadale
Government funding to School Resourcing Standard: 131%
Annual over-funding: $540,000

Al Siraat College
Government funding to School Resourcing Standard: 131%
Annual over-funding: $1.5 million

Christ Church Grammar School, South Yarra
Government funding to School Resourcing Standard: 131%
Annual over-funding: $230,000

St Catherine's School, Toorak
Government funding to School Resourcing Standard: 121%
Annual over-funding: $310,000

ACT: most over-funded private schools 

Radford College
Government funding to School Resourcing Standard: 203%
Annual over-funding: $4.9 million

Daramalan College
Government funding to School Resourcing Standard: 193%
Annual over-funding: $7 million

Marist College
Government funding to School Resourcing Standard: 178%
Annual over-funding: $6.8 million

* excluding schools focused on special needs