A firefighters fraternal group called The Vulcan Society has proposed to Jude Nicholas Garaufis that the department should be forced to make six of every 10 new hires either black or Hispanic.
City lawyers say the plan would be unconstitutional.
The Justice Department has taken the city to court over the FDNY's hiring practices, saying its recent entry exams discriminated against minority candidates.
But federal authorities have also asked the judge to reject the Society's proposal, saying it is too broad.
Last year, Garaufis ruled that two prior FDNY entrance exams were biased against hundreds of black and Hispanic applicants. On those exams, fewer than 10 percent of the candidates were black or Hispanic.