Public school districts receive the bulk of their funding from the state, mostly in the form of a flat fee based on student attendance.
Brown's proposed budget for the 2013-14 budget year, which begins July 1, is expected to include a weighted formula that would pay more for students in districts with high numbers of poor students or students who don't speak English at home.
Brown has also indicated a desire to loosen restrictions on dozens of special programs - everything from adult education to class-size reduction grants - potentially freeing up billions of dollars to be spent by local districts.
"This is one of the most significant policy and fiscal changes we've seen in education in recent memory," said Edgar Zazueta, the chief of government relations for Los Angeles Unified.
This would be Brown's second attempt to change how California allocates money for K-12 education, which makes up about 40 percent of the state budget.
Last year, lawmakers representing well-off suburban districts objected to the plan, fearing the loss of revenue to their cash-strapped counterparts. The formula the governor proposed last January factored in the number of disadvantaged students in a district, with additional money allocated to those where more than half of the kids are poor or not fluent in English.
Los Angeles and Long Beach Unified school districts, where nearly 90 percent of the students are English-learners or low income, would have received $3,000 more per student.
Districts with lower concentrations of disadvantaged students would have received a proportionally smaller premium.
Officials cautioned those figures are outdated, and the funding formula now being finalized is likely to be significantly different.
Ron Bennett, of the School Services of California, which advises school districts on the state budget, said he expects the governor to unveil a "kinder and gentler student formula."
Bennett estimated that the state could give schools from $2 billion to $2.5 billion more in the next fiscal year than they received this year. That would allow the governor to begin phasing in the new funding formula without hurting some schools, he said.
The proposed changes are getting a mixed response from legislators.
"I would be open to looking at any proposals that would change how funding is currently done. I don't think the system that we currently have is working for school districts," said Assemblywoman Norma Torres, D-Chino.
"More often schools in poor areas have children with terrible disabilities and have big disadvantages. More money for those districts is a good option to look at."
Assemblyman Curt Hagman, R-Chino Hills, cautioned that school districts that get more money are generally the ones that perform the worst.
"I've seen them try to sign students up for after-school dinners, lunches and breakfasts because they get more money. ... We've given teachers so much slack, they teach less hours for the most amount of pay in the nation, and we wonder why we get bad results," Hagman said.
But he likes the other half of Brown's proposal, which would free up local school boards to spend their funds more freely.
"I like giving locals control," he said. "I always have, always will."
Assemblyman Mike Gatto, whose 43rd District includes part of LAUSD along with Burbank, Glendale and La Ca ada Unified, said he expects the debate to be even more intense this year.
"We have to make sure that we strike a balance," said Gatto, D-Burbank.
"We as policymakers need to put aside our parochial interests and do what's good, with a capital G, for the long-term future of the state."
School districts at the local level are likewise also mixed in their responses.
"If there's less money for us, as a board member for Upland Unified District, I'm obviously not thrilled about that," said Wes Fifield, president of the Upland Unified school board.
Fifield's relatively affluent, successful district seems likely to receive fewer funds under the new proposed formula.
"Throwing money at it doesn't always solve the problems, but it does help a little bit," he said.
"There's a two-edged sword, because if you do well, and work with your staff, and place close monitoring on benchmarks and student achievement, you are essentially penalized for doing better," said Steve Garcia, an Ontario-Montclair School District school board member.
His district would likely get more money under a weighted student formula.
"You could conceivably say `Well, if we don't do well, we'll get more money for our schools next year.' I could see some abuse with that, personally," he said.
"I think you need to reward schools that are doing better and are managed better."
Among the suburban districts that could be given short shrift by Brown's proposal is Torrance Unified. Torrance is in the position of potentially being the neglected middle.
On the one hand, when compared against statewide averages, it has a much smaller percentage of poor students and English learners. On the other, it is a large district that doesn't have the parent-fundraising power of smaller centers of affluence, such as Manhattan Beach.
George Mannon, superintendent of Torrance Unified, is among the leaders of suburban districts who publicly objected to Brown's earlier proposal.
"The way the formula was designed, you were going to have winners and losers," he said.
"The winners would be large urban districts. ... In our area, we were all losers."
But Mannon added that he is withholding judgment on Brown's amended proposal until the governor releases more details.
Michael Kirst, president of the state Board of Education, who drafted a weighted student formula plan back in 2007, disputed that some schools would lose money to boost funding for others.
"There never was a proposal to take money from schools and give it to other schools," Kirst said. "All schools are to increase in their amounts. They'll just increase differently."
Brown is expected to unveil his 2013-14 school budget next week.
Staff Writer Rob Kuznia and the San Jose Mercury News contributed to this report.