With the state and New York City on a collision course over how to resolve the long-running Campaign for Fiscal Equity lawsuit ordering $23 billion in additional funds for the city’s public schools, some budget experts are suggesting a deal.

The idea is for the state to absorb the city’s Medicaid costs and for the city to spend the savings on school operating aid to resolve the lawsuit.

The exchange would involve roughly the same amount of money: State courts have said the state owes the city school system at least $4.7 billion a year to meet its constitutional education funding obligations. The city’s Medicaid bill for this fiscal year is also about $4.7 billion.

A similar transfer would also take place outside the city — in Long Island and upstate New York, where local governments are contributing more than $2 billion to Medicaid. The state again would pick up the tab from the county governments, which would then direct the freed dollars to relieve property taxpayers or to support their local school districts.

The idea is in rough form and has its share of skeptics. One key question is how the state government could afford to cover the local government Medicaid share. Another is how county governments outside the city would be required to spend the money. But the idea is getting serious attention from public policy experts in the city and in Albany who have long been critical of the state’s Medicaid funding system, which requires many cities and counties to pitch in for the costs of Medicaid.

“It would be a fine idea,” a former budget director for the State of New York and for the New York City Board of Education, Dall Forsythe, said. “The trick is to find out how it would work for all of the cities and counties in New York that have to pay a share of Medicaid.”

Proposals for a Medicaid swap have floated around Albany since the days of the Carey administration. In 1991, Governor Cuomo offered to take over the local share of Medicaid in exchange for a portion of county sales tax revenue.

Those who have advocated a state takeover of Medicaid now view the Campaign for Fiscal Equity lawsuit as an ideal vehicle for a swap. For more than a decade, the state government has been battling the lawsuit, which claims the state is violating the state Constitution by under-funding New York City public school students. With the appeals process winding down, next year’s governor will almost certainly be grappling with a settlement.

“Sometimes you dust off a new idea and apply it to a new set of issues,” the originator of the swap idea, William Cunningham, said. “The reason why politically this could work is because everybody benefits at the same time.” Mr. Cunningham is a former top aide to Mayor Bloomberg and is now a managing director at Dan Klores Communications.

The Democratic candidate for governor, Attorney General Eliot Spitzer, says he would deal with Medicaid, property taxes, and the lawsuit separately.

Mr. Spitzer has said he intends to quickly settle the lawsuit and is proposing that New York City public schools receive between $4 billion and $6 billion in additional annual operating money. He’s been silent, however, on what portion of the money would come from the state. He’s also proposing to shift $6 billion of state funds over three years to local school districts to offset property taxes. He says he will save money on Medicaid by reducing long-term care and prescription drug costs.

Some policy specialists say a bundling Medicaid and the lawsuit could make more sense.

“It’s true that if we got some Medicaid relief, we would be able to support the schools and still not impose a very heavy tax burden,” said Charles Brecher, the director of research for the Citizens Budget Commission. “It works for the city to combine the two. The problem is for the rest of the state.”

New York is one of the few states in the nation that requires its local governments to pay a significant share of the Medicaid program. After the state imposed a cap on local share growth at 3%, the local government share has dipped to about 18% of the total program’s cost. The federal government pays for half.

Public policy experts have argued that large entitlement program expenses like Medicaid ought to be spread over a wide as possible tax base.

Under the existing arrangement, they argue, local governments in New York with greater numbers of Medicaid recipients are put at a comparative disadvantage. “Forcing localities to bear a substantial portion of what in most other states is a state-level burden results in higher local taxes in localities with concentrations of Medicaid-eligible residents,” said a January report published by the publicly funded New York City Independent Budget Office.

Proponents of a Medicaid swap also say it would hold the state government more accountable by shifting expenses to the governor and lawmakers who are responsible for setting policy and to some extent determining the cost of the program. The effect, they say, would be to give the state government more of an incentive to cut out waste and fraud from the system and make it more efficient.

“It does shift responsibility and accountability in the right direction,” said the director of the fiscally conservative Empire Center for New York State Policy, E.J. McMahon. “But it still begs the question of how you phase this in. Where does the money come from?”