Four panel members voted against granting the waiver, two voted in favor, and two voted "not at this time," according to state officials.
Black needs a waiver from the state because she does not have a background in education.
The waiver would allow her to her bypass the prerequisites, which include a degree in education and experience as a teacher.
State Education Commissioner David Steiner still has the final say in whether Black gets the job.
She would replace Joel Klein, who is leaving to take a job with News Corp..
However, The Wall Street Journal reports that Steiner has "serious concerns" about granting the waiver, citing a person familiar with his thinking.
The commissioner, however, would be more open to granting a waiver request if it includes a plan to pair Ms. Black with a strong deputy with educational experience, this person said.
"I will weigh their advice and insight as I consider the decision before me," Steiner said in an official statement.
Mayor Michael Bloomberg selected Black for the post. A poll released Tuesday shows she is not a popular choice.
The Quinnipiac University Poll released Tuesday shows New Yorkers believe by a 2-1 margin that Black is not qualified for the job. The poll found that 51 percent of New York City voters believe Black does not have the right experience to serve as schools chancellor. Just 26 percent said Black does have the experience for the job, and 23 percent were undecided.
Asked specifically about Black's appointment, 47 percent said they disapproved and 29 percent approved. Twenty-five percent were undecided.
"If it was a public vote, thumbs down," said Maurice Carroll, director of the Quinnipiac University Polling Institute.
But foes and supporters of Black's appointment have been lobbying him since Bloomberg announced on Nov. 8 that he had chosen the 66-year-old Black to succeed Klein.
The city Department of Education released a letter to Steiner on Tuesday, backing Black's appointment and signed by 28 high-profile women including Whoopi Goldberg and Gloria Steinem, with whom Black worked at Ms. magazine in the 1970s.
"We are delighted that the largest public school system in the country will, for the first time, be headed by a woman - and in Cathie Black we have an extraordinarily qualified and visionary leader," the prominent women said. "We urge you to grant the necessary waiver for this historic appointment."
Last week, former mayors Ed Koch, David Dinkins and Rudy Giuliani sent Steiner a letter in support of Black.
Thousands of New Yorkers have signed online petitions opposing the waiver for Black, and some City Council members and state legislators have urged Steiner not to grant the waiver.
Bloomberg has said that Black is the right person to raise achievement levels for New York's 1.1 million public school students because of her track record as a top media executive.
But the Quinnipiac poll found that New Yorkers are skeptical, with 64 percent saying that a schools chancellor needs education experience more than management experience.
The survey of 1,287 New York City registered voters was conducted Nov. 16-21. It has a margin of error of plus or minus 2.7 percentage points.
A Bloomberg spokesman did not respond to a request for comment on the poll.
Some information from The Associated Press
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