Mr. Bratton did not respond to a request for comment.

“As New Yorkers, it’s incumbent on us to keep making sure Times Square is keeping up with the times, and doesn’t go back to what I’ll call the bad old days of the ’70s or the early ’90s,” said Marc Holliday, the chief executive of SL Green. “And we all remember what that was like, when it comes to crime, and, you know, open drug use.”

The casino is expected to include a hotel, a wellness center and restaurants, right above the Broadway theater that is home to “The Lion King” musical and a stone’s throw from the site of the ball drop on New Year’s Eve.

Earlier this year, the state authorized up to three casino licenses for the New York City region. Legislators have touted the union jobs, tourists and tax revenue that a casino would attract, citing the fact that the bidding for each license will start at $500 million.

Two existing “racinos” — horse racetracks with video slot machines but no human dealers — are considered front-runners for two of the three licenses: Genting Group’s Resorts World New York City in Queens and MGM Resorts International’s Empire City Casino in Yonkers, N.Y.

The competition for the third license features many of the country’s major casino companies. Steven Cohen, the owner of the New York Mets, has been talking with Hard Rock about a casino near the baseball team’s stadium in Queens. Las Vegas Sands has been finalizing plans for its preferred casino location in the area, and Bally’s Corporation has been scouting for a development partner.

The Wynn-Related proposed casino would be on the undeveloped western portion of the Hudson Yards, which was supposed to be completed by 2025 and include residential units and parks. Related, the developer of Hudson Yards, said it plans to fulfill all of its prior housing and public space commitments for the area.

In a private pitch deck obtained by The Times, Wynn and Related wrote that Hudson Yards, near the Javits Center, was the ideal location to target “diverse upscale” guests for a casino resort complex.