ALBANY – In the quest to make New York State the Nevada of the East, Gov. Andrew M. Cuomo is pushing his casino-expansion effort in his newly proposed state budget.

Using the budget process gives him the upper hand in negotiations with the State Legislature, which has less budget-making power than New York governors.

With New York already among the nation’s top gambling centers, Cuomo’s budget plan defines how he believes the initial phase of a casino-expansion effort should be undertaken if voters approve a statewide referendum this fall.

The governor has said he wants the initial three casinos – of seven he wants built on non-Indian lands – to be located upstate as an economic-development boost. While Cuomo is keeping his cards close to the vest, there has been speculation that the first casinos could be located in the Catskills, the Saratoga Springs area and the Adirondacks.

An examination Wednesday of the finer details of his proposed 2013 budget shows that the governor has now defined “upstate,” though he is still not specific about where the casinos should be built.

The new budget plan would prohibit the first three casinos from being built in New York City, Long Island or Westchester, Putnam and Rockland counties. He does not specifically state that none of the three casinos would be in Western New York, as he previously had suggested.

Cuomo said Tuesday that his plan to restrict the initial round of casino expansion to upstate is “one of the most exciting opportunities” the state has to help upstate New York. The Legislature last year gave first approval to a constitutional amendment that would allow up to seven casinos on non-Indian lands. If lawmakers approve the measure again, it proceeds to a November referendum.

The proposed casino amendment does not address where future casinos would be located. Lawmakers say they want to be more specific in the separate, “enabling” legislation so that all seven sites are identified at least by regions. That could pose a problem for Cuomo’s idea to limit the first three to upstate, which he says needs an economic jump-start.

But if the initial round of casino construction were allowed to be open statewide, casino developers might want to build new gambling halls only in New York City.

Cuomo recently suggested that the large area of Western New York – essentially all the area west of state Route 14, between Rochester and Syracuse stretching from Lake Ontario to Elmira – would not be open for new casino development. That is because the Seneca Nation, in its 2002 compact with the state, has an exclusive right to operate in that zone with its three casinos in Niagara Falls, Buffalo and Salamanca.

But Cuomo left some wiggle room, saying he would “honor legal agreements that are in good standing.”

Whether the 2002 compact remains in “good standing” is in question because the state and the Senecas have been at odds for several years, with the tribe contending that the state violated the compact by permitting new forms of gambling in the region, such as casino facilities at racetracks. The Senecas have withheld more than $500 million in revenue-sharing payments to the state, and the matter is in arbitration. No one knows whether the compact will be honored by either side.

The budget that Cuomo proposed this week makes no mention of banning new casinos from areas such as the exclusivity zone held by the Senecas. The new casino language in the budget plan leaves it to a new state Gaming Commission, being formed Feb. 1, to pick the operators and locations.

The governor’s legislation also states that prospective casino operators should show that they have “significant support” from local governments and communities that might be home to any new casinos. The language is vague about how such support will be shown, but Cuomo has dismissed the idea of allowing localities to hold separate votes – as has been done in some other states – to determine if a community wants a casino development.

Cuomo’s legislation stipulates that 90 percent of any proceeds from the casinos go into the state’s dedicated funding for public schools, with a separate 10 percent allocated for property tax relief in the host localities.

Since Cuomo floated the idea of putting the first three casinos at some unknown locations upstate, critics have said that it is inappropriate to ask voters statewide to consider a major gambling expansion without being told at least the general locations of all seven casinos.

Not knowing where future casinos would be located “is a concern of mine, and it’s also going to be a concern of any potential investor not knowing if there’s the possibility of competition being located nearby,” said Assemblyman J. Gary Pretlow, D-Mount Vernon, chairman of the Racing and Wagering Committee. Pretlow wondered why a casino developer would invest several hundred million dollars in a multiyear planning and construction effort if, down the road, new competition would be permitted nearby.

Pretlow believes that voters will approve a referendum if the Legislature gives second approval to the constitutional change to permit full-blown casinos – including table games, such as poker, now banned at racetrack casinos. “But I think it would be a lot better if that referendum had enabling legislation behind it, showing where all the casinos were going to be,” he said.

New York already has nine racetrack-based casinos, as well as six Indian-owned casinos and an ever-expanding state Lottery program.

Cuomo, in his budget plan, wants to lift restrictions that were imposed on the controversial Quick Draw game when it was introduced in 1995. The Cuomo administration, in its proposed budget, argues that the game “has proved no more likely to be abused than other lottery games.”

Among the last restrictions that Cuomo wants lifted are a ban on establishments, such as bars, that do not have at least 2,500 square feet of space and the current law that requires someone to be at least 21 years old to play Quick Draw on premises that serve alcohol. Lottery games would still be illegal for those younger than 18.

The budget plan says lifting those restrictions would “strengthen the game’s ability to produce additional sales and earnings.” Cuomo estimates that the Quick Draw plan will generate $24 million annually in revenues to Albany.

Putting the casino-expansion language into the bill gives an edge to Cuomo because lawmakers cannot unilaterally change his “language bills’’ that describe budget policies. If Cuomo wanted to, he could force lawmakers to choose between taking his plan or forcing a government shutdown. It is a route he is also taking with his plans to raise the minimum wage.