Ever since the city and state paid the federal government $1 for an island in New York harbor, officials have wondered what to do with it. Mayor Bloomberg floated a new idea today: spending his own money to create a public health center there.

The billionaire and longtime philanthropist who gives away multimillions each year has recently begun shaping his official charitable foundation. He suggested on his weekly radio show that the foundation could lease some of the historic buildings on the 172-acre Governors Island and create an international campus dedicated to public health.

Visiting scholars would come and study together, hold conferences, and present research, he said.

“Something that pulls together — where you’d have a conference on malaria, let’s say, and there’d be papers presented and people from around the world would come and could actually stay there on the island in these old houses and use one of the buildings for dining rooms and meeting rooms and presentations.”

The island, about half a mile from lower Manhattan and accessed by ferry, is virtually uninhabited now, apart from a firehouse, small security operation and staff from the National Park Service, which still owns and operates 22 acres there. A new high school is set to open there next year, funded by the Bill & Melinda Gates Foundation.

The island served as a British and then American military base for more than 200 years. Captured Confederate soldiers were imprisoned there during the Civil War, and it was an Army supply base during World Wars I and II. Landfill from the excavation of the Lexington Avenue subway was added in the early 1900s, forming 103 acres of its total area.

The federal government ceded most of the land to the city and state in 2001, but since