One is to stay in the Mitchell-Lama program and negotiate some financial relief from the state.
One city official said that property taxes would increase by at least $12 million if the complex left the Mitchell-Lama program.
It is the largest complex built by the state under the Mitchell-Lama program, which sets aside housing for middle-class families.
Those defaults played a role in the city and state fiscal crisis of 1975, when the Mitchell-Lama program ended.
So far, five projects throughout the state have left the Mitchell-Lama program.
During the last five years, about 13,000 housing units across the city have been withdrawn from the Mitchell-Lama program.
They also fear that the landlord plans to buy out of the Mitchell-Lama program and raise rents.
The buyout process under the Mitchell-Lama program usually takes nine months to a year, officials say.
The 12-story building was built in 1965 under the state's Mitchell-Lama program to house nurses and administrative workers.
So far 20 of the 421 projects built under the Mitchell-Lama program have been removed.