Officials at the city's Department of Housing Preservation and Development say the city is requesting more information from One57 on their application. They said the building's two applications for the tax breaks – one for the condo section and one for the rental section of the building – are "incomplete" and they have requested more information.
The department declined to give specifics on what information is being requested, or whether the request is procedural or relates to the substance of the application.
The developer behind One57, Extell Development, didn't return calls and emails for comment.
One57 has become a symbol of hyper-priced real-estate in New York, with billionaires paying $90 million or more for at least two of the building's penthouses. It's projected to be the largest residential tower in New York when it opens next year. (Read more: Billionaire Tower Gets 'Low-Income' Tax Breaks )
According to financial documents obtained by CNBC, One57 planned on a tax abatement under a long-existing city program designed to provide more low-income housing. The program, known as 421-a, gives developers tax breaks for 10 to 20 years, which are then passed on to buyers. At One57, those savings may be substantial.
The program requires buildings to allocate at least 20 percent of their units to low-income families, in return for tax breaks of up to 80 percent for the first two years.
One57 used a popular loophole in the law that allowed the developers to take the tax benefit for the building overlooking the park, but fund the affordable housing units in another location. One57 bought credits or "certificates" that helped fund those affordable housing units in outer bouroughs, according to city records. (The loophole has sinced been closed). (Read more: CEO to Workers: You'll Likely Be Fired If Obama Wins )
The tax savings for the top 13 floors at One57 add up to more than $1.5 million a year, according to the documents. The tax savings are in effect for two years, then are reduced by 20 percent every two years for 10 years, according to people familiar with the building.
Gary Barnett, founder of Extell, said in a previous interview that the building has followed all the guidelines for the program, and that through the 421-A program, One57 has helped build "countless" affordable housing units in the Bronx, Brooklyn and elsewhere.
"We've done exactly what the program was intended to do, which is to create affordable housing, " he said. "We've had some benefit because of the abatements, but the real benefits have been to affordable housing, " he said.
-By CNBC's Robert Frank
Follow Robert Frank on Twitter: @robtfrank