CANBERRA, June 14 - The minor party set out its demands on Wednesday in a dissenting report attached to a government-dominated Senate committee report which called for the bill to be passed.
The Greens' nine votes will be crucial to the legislation passing, given Labor's opposition to it.
The party is demanding underfunded schools get an increase in funding over a shorter time frame than the government's proposed 10 years.
State and territory governments would be "tied" to the reforms, requiring them to bring public schools to the new resourcing standard.
An independent national schools resourcing body would act as a watchdog, overseeing and reviewing all aspects of schools funding including the resourcing standard.
And conditions relating to teachers, principals, curricula and school testing currently being undertaken by scheme architect David Gonski must be kept independent of any changes to needs-based funding legislation.
"Instituting a genuine Gonski model of funding is critical for our children," Greens education spokeswoman Sarah Hanson-Young said in the report.
Gonski briefed the Greens party room in Canberra on Wednesday, ahead of the legislation being debated in the Senate next week.
Asked whether the independent watchdog, which is not in the legislation, was a deal-breaker, Senator Hanson-Young told Sky News: "It's one of the key elements of the Gonski plan. I don't see how the Greens could agree to a package that doesn't put in place genuine independent oversight."
Crossbench senator Nick Xenophon has similar concerns to that of the Greens and wants a shorter time frame than 10 years for the delivery of the extra $18.6 billion.
The committee noted in overall terms federal schools funding would rise to a record $242.3 billion over the decade to 2027, or about 4.1 per cent annually for every Australian student over 10 years.
"The aim of the bill is to ensure that school funding across Australia is based on need, and is allocated fairly between states, schools, and sectors. The committee is satisfied that the bill will achieve these goals," the report concluded.
Labor agrees with needs-based funding but says the figure is $22.3 billion less than it planned.
The opposition said in its dissenting report the new system would result in 85 per cent of public schools being funded below their schooling resource standard in a decade.
"The bill should not be supported in its current form," the Labor report concluded.