ALBANY — Gov. Andrew M. Cuomo, in his budget address on Tuesday, is expected to propose setting aside $1.5 billion over five years to pay for an expansion of prekindergarten classes statewide, administration officials said.

The proposal by Mr. Cuomo is likely to be seen as an attempt to outmaneuver the newly elected mayor of New York City, Bill de Blasio, whose signature campaign proposal was raising taxes on the city’s highest earners to finance an expansion of prekindergarten and after-school programs.

The program would be a broad one: School districts across the state would be eligible, and the state would fund a school district’s prekindergarten plan once the state has reviewed it and determined it is feasible, one of the officials said. The officials requested anonymity to discuss the proposal in advance of Mr. Cuomo’s budget proposal.