Bredesen, who has said he wants to improve and simplify the state's funding formula for K-12 schools, held meetings with Democratic lawmakers about the plan on Monday.
The governor's plan would be phased in over several years and would eventually cost more than $560 million a year, The Knoxville News Sentinel reported Tuesday.
Officials declined to discuss details about the program with reporters, though one uninvited reporter was allowed to sit through Bredesen's presentation.
As much as $283 million could be added to the funding formula in the budget year that begins in July.
"That's something we can possibly stretch to," Bredesen told the Democratic leaders. Higher-than-expected revenue collections could help cover the increased costs.
State and local governments share K-12 education expenses under a complex formula called the Basic Education Program, or BEP. It was created in 1992 after courts ruled the state's old formula unconstitutionally deprived children in poorer counties of an adequate education.
Bredesen has cited funding problems for school systems in Knox and Hamilton counties as examples of how the BEP has "become a little long in the tooth." Officials from those two counties have been among the most vocal about what they consider the shortfalls of the formula in funding their districts. The elements of Bredesen's proposed changes to the BEP include: â€¢ Having the state to pay 75 percent of teacher salaries instead of the current 65 percent. â€¢ Replacing a complicated "cost differential factor" used as a sort of cost of living index with one based on property and sales tax collections. â€¢ Increasing the state funding for English language instruction to pay for one instructor for every 35 students, instead of the current 45. The revisions to the BEP would be "based on common sense rather than a lot of fancy computer programs that nobody understands," Bredesen said. Bredesen said the changes to are contingent on the passage of his proposal to boost education spending through a 40-cents-per-pack increase in the state cigarette tax. Most projected $220 million revenues from the cigarette tax hike would be directed toward K-12 and higher education. "If you don't get the cigarette tax increase, you don't get enough water to raise all boats," Finance Commissioner Dave Goetz told the Democratic group. The governor wants to use $120 million of the cigarette tax money to help school districts pay for the extra costs of educating "at-risk" students - those who qualify for free or reduced school lunches. Another $27 million would go toward bridging a funding gap for districts that have a large growth in student population. An additional $48 million would be used in higher education to try to keep annual tuition increases below 7 percent, and $21 million would pay for agricultural grant programs.