FILE - In this Tuesday, Sept. 10, 2013 file photo, New York Democratic mayoral candidate Bill de Blasio embraces his son Dante, left, daughter Chiara, second left, and wife Chirlane McCray after polls closed in the city's primary election in New York. De Blasio and his wife settled in the Park Slope neighborhood of the Brooklyn borough of New York largely because they felt that their interracial relationship would be accepted there, the mayor-elect has said. (AP Photo/Kathy Willens, File) ( Bill de Blasio embraces his son Dante, left, daughter Chiara, second left, and wife Chirlane McCray on Election Night in September. (AP Photo/Kathy Willens)

(Update: Statement from Darling-Hammond)

New York City Mayor-Elect Bill de Blasio is considering a number of candidates to be his new public schools chancellor —  a decision that is one of the most visible and important he will make as he staffs his new administration — and it seems like every day there is a new rumor about who is still on his list and who isn’t.

The de Blasio transition team hasn’t said anything publicly about any specific candidates,  though the mayor-elect told The Observer Sunday that he was taking his time to make a decision:

I think by definition, education chancellor is one of the most crucial decisions to make, but that doesn’t mean it will be the next announcement. But it’s very much on our minds all the time. I think, you know, by the end of this week we’ll have some important additional announcements, but it will not necessarily be that one.

During the campaign and even earlier, de Blasio had made statements in opposition to the corporate-influenced reform policies of Mayor Michael Bloomberg, saying that the city had enough charter schools and that standardized testing was “poisoning our system.”

Among the people who have been considered at one point or another in the decision-making process are, according to sources, Joshua Starr, Montgomery County Public Schools superintendent, who has good union relations and who became nationally known when he called for a three-year moratorium on standardized testing last year; Carmen Farina, a former superintendent of a New York district when de Blasio was a school board member and who has long been an advisor to the mayor-elect; Kathleen Cashin, a member of the New York State Board of Regents and a former teacher and district superintendent.

Kaya Henderson, the chancellor of schools in Washington D.C., was thought to be an early candidate and de Blasio and Henderson had a phone conversation, but sources say de Blasio would not select her because she supports the kind of school reform he has criticized. Other names have popped up too, along the way, including Chicago Public Schools Chief Executive Officer Barbara Byrd-Bennett, and Andrés Alonso, the former chief executive officer of Baltimore City schools who resigned last summer after six years and who was a deputy chancellor in New York before going to Baltimore. Some have suggested that if de Blasio really wanted to make an unexpected statement about supporting teachers and improving labor relations, he would pick American Federation of Teachers President Randi Weingarten, though she supported a rival in the mayoral campaign. Weingarten, incidentally, was suggested as D.C. schools chancellor a few years ago by none other than my colleague, the great education writer Jay Mathews.

Other names have popped up too, but there is one person who, knowledgeable sources say, de Blasio really wanted and could not get: Stanford University Professor Linda Darling-Hammond. Darling-Hammond, a giant in the education world,  directs the Stanford University Center for Opportunity Policy in Education and was founding director of the National Commission on Teaching and America’s Future. A former president of the American Educational Research Association and a member of a long list of blue-ribbon committees and other panels, Darling-Hammond was the head of education policy on Barack Obama’s transition team when he won election as president in 2008. Many believed she would be selected as secretary of education but Obama selected Arne Duncan, the former CEO of Chicago public schools who was preferred over Darling-Hammond by people who were pushing for reform that treated public education as a business rather than the civic institution that it actually is.

The job was Darling-Hammond’s, but she declined, sources said. That led to the selection process that continues.

Darling-Hammond issued a statement Monday that said:

It has been reported that I declined an offer to serve as Chancellor of the New York City schools. I did not seek nor was I offered this position. I look forward to learning who the next chancellor will be and to supporting his or her work on behalf of New York City’s children.