Crews have inspected the crane, though they had no plans to try to remove it, according to Lewis Colletti, CEO and president of the Building Trades Employer Association, which represents construction companies in New York City.
"Efforts to dismantle the crane at this point would provide more of a danger," Colletti told CNBC on Monday.
Colletti said that construction companies throughout the city, including this project, have been working with the buildings department since Friday in securing to the best degree that anyone could in preparation for Sandy. All construction sites were supposed to be secured and closed as of 5 p.m. Saturday.
Recently, Extell, the developer for the project, has come under scrutiny for its use of a city program that grants deep property-tax abatements in exchange for providing low-income housing.
There are no low-income residences at One57, however. As CNBC's Robert Frank reported in earlier this month, "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."
City officials now say they are requesting more information from Extell before approving their application to the program. (Read More: City Scrutinizes Tax Breaks for Luxury Tower)
The Associated Press contributed to this report.