The depiction of the women and the man, “as though they are vice and he is virtue,” is a problem, Helen M. Marshall, the Queens borough president, said. “That statue is 90 years old and that kind of thinking is far-off and crazy.”

Last week, the statue, which was designed in Paris by Frederick MacMonnies and sculptured of white Georgia marble in the Bronx, still stood in its fountain on Queens Boulevard, behind a chain-link fence, while the Department of Citywide Administrative Services, which oversees it, considered what to do with it. One option might be Green-Wood Cemetery, in Brooklyn, a national landmark that has offered to accept it, according to a spokeswoman for the department.

That the statue may end up amid graves is not a concession to those who, over the years, have wanted it proverbially dead. After watching a televised news conference last year in which Anthony D. Weiner, then a congressman, suggested the work, which weighs 22 tons, should be sold on Craigslist, Richard J. Moylan, the president of Green-Wood, became incensed.

“That just infuriated me,” said Mr. Moylan, who is a former treasurer of the National Sculpture Society. “Whether you like it or not, it’s art. You don’t destroy art.” He offered the cemetery as a home for the husky sculpture, also known by fond monikers like Rough Boy, Fat Boy and Cave Man.

Several of Mr. MacMonnies’s relatives are buried at Green-Wood, Mr. Moylan added, and there is a frieze of pink granite by the artist himself memorializing one of his friends. The statue would be placed near the cemetery’s front gates, he said.