Mayor Eric Adams’s chief of staff, Frank Carone, recently met Las Vegas Sands’s chief executive Robert Goldstein at Mr. Goldstein’s Upper East Side pied-à-terre. Mr. Adams, who as a state senator led the gaming committee, wants New York City to get two of the three licenses the state is poised to authorize, his spokesman said, rather than see one of them end up in, perhaps, Long Island. His aides have spoken with several other casino operators, too.

Many lawmakers and lobbyists in Albany believe that two of the licenses are likely to be awarded to MGM and Genting, which operate the two so-called racinos — horse racetracks that have been refashioned as casino-like properties, albeit without games like blackjack or roulette — in Yonkers and Queens, which already employ thousands of union members.

Both facilities have ties with local stakeholders and could begin operating as full-scale casinos in a matter of months, quickly generating up to 5,000 new jobs and hundreds of millions of dollars in tax revenue for the state. Indeed, both companies have struck agreements with the Hotel and Gaming Trades Council to make a priority the hiring of hotel workers who underwent a union training program to become food service and maintenance workers.

State Senator Joseph Addabbo Jr., a Democrat and chairman of the committee that oversees casinos, said that awarding two of the licenses to MGM and Genting “is probably the most popular scenario, with nothing being a given, because it should be an open process.” Genting’s Resorts World Casino is in his district.

The competition for the third, and possibly only unclaimed license, has spurred a lobbying frenzy, with pitches ranging from a casino next to the Water Club on the East River to what State Senator Liz Krueger, a Democrat from the Upper East Side helping lead state budget negotiations, describes as “a fancy Monaco-like casino on the top floor of Saks.”

A spokeswoman for Saks declined to comment.

“The third casino shouldn’t go anywhere but Manhattan,” said Michael O’Keeffe, the owner of the Water Club, who argued Manhattan is ideal for a small, high-end, Monte Carlo-style casino that will cater to a different market than casinos in Queens and Yonkers. “There’d be no taking money away from poor people who can’t afford to gamble.”

The flurry of proposals for a Manhattan casino carries no guarantee of success. Legislators are likely to require some semblance of local approval for a casino, and opposition among local legislators in Manhattan runs high.