The governor's administration estimates that the state could get $530 million over two years by selling off the rights to the proceeds.
Lawmakers balked at the idea last year because the money is currently committed to funding children's programs, such as Early Head Start. The governor's budget proposal would fund these programs through the general fund through 2019.
In addition to the tobacco settlement, the governor wants to sweep $596.8 million from the state's highway fund over a 2 1/2-year period.
Brownback has repeatedly swept money from the highway fund in recent years, which has forced the Kansas Department of Transportation to cancel and delay projects.
Brownback also hopes to save $120 million over a two-year period by merging school district health plans under one state-run plan, a change that was recommended by efficiency consultants last year.
Brownback's proposal, which would be mandatory, could face backlash from educators.
Right now most school districts control their own health plans and some districts have used more generous health benefits as a recruitment tool.
Brownback also hopes to save $16 million over two years by requiring school districts to purchase goods through a joint procurement program.
The governor hopes to save about $750,000 over two years by merging the state's securities commissioner's office with the Kansas Insurance Department.
Brownback is also proposing increasing the privilege fee for managed care organizations from 3.31 percent to 5.77 percent and the hospital provider tax from 1.83 percent to 4.65 percent.