[UPDATE (Nov. 17): Trump’s transition team told reporters that the president-elect met with Moskowitz at Trump Tower in New York City Wednesday to discuss a position in the administration. However, the New York Times reported early Thursday that Moskowitz had taken herself out of the running for the job.]

We mentioned recently that ex-District of Columbia schools boss Michelle Rhee and Success Academy Charter Schools founder and CEO Eva Moskowitz are rumored to be candidates for secretary of education under President-elect Donald Trump. Politico reported Wednesday that Moskowitz is officially in the running.

And Trump transition team spokesman Jason Miller mentioned them on MSNBC Wednesday in the video clip below, starting at about the 4:15 mark:

In addition to the many Republican stalwarts mentioned as possible candidates for education secretary, such as Rep. Luke Messer of Indiana and Gov. Scott Walker of Wisconsin, Rhee and Moskowitz certainly stand out. So what are a few incentives for Trump to appoint either of them as his top education official, and what are the reasons he wouldn’t? And how would Trump’s appointment of Moskowitz or Rhee impact the school choice world, and the charter school community in particular?

Eva Moskowitz

Moskowitz was an elected Democrat on the New York City Council for several years. So she might not get the glad-eye from many Republicans, either in a confirmation process or in general. However, Success Academies has gotten donations from hedge fund executive John Paulsen, who also donated to Trump’s campaign. So she might have the kind of high-level entrée to GOP politics that could help her—if she wants the job. And like Trump, Moskowitz is a New Yorker, with a reputation for speaking her mind.

Success Academies has passionate supporters, who say the schools can show strong academic results for students from disadvantaged backgrounds—a claim the charter school network’s fierce opponents say is misleading, and ignores concerns about the climate for some students at Success Academies schools. Would Moskowitz have the freedom to bring her approach to charter school instruction and expansion to the Education Department?

Here’s one of the broadest questions for the education community: How would charter school advocates react to a Secretary Moskowitz?

On the one hand, some in the charter community could be thrilled to have one of its biggest names work in a presidential administration. On the other hand, charter schools have grappled with complex questions recently about their relationships with minorities and the schools’ place in minority communities. Think of the NAACP’s recent vote in favor of a moratorium on new charter schools, for example.

So how would advocates react if one of their own agreed to work for a president-elect many opponents believe exploited racism and racial divisions to win the presidential elections? And what would her appointment signal to critics of Moskowitz’s work?

Michelle Rhee

Until a few years ago, Rhee identified as a Democrat, but she said she broke with her party because of her support for vouchers. She didn’t officially join the GOP when she publicly left the party in 2013, but Republicans in Washington could quickly throw cold water on the idea of Rhee actually getting confirmed.

However, if Trump is serious about using $20 billion in federal aid to create, essentially, a new federally backed voucher system, Rhee could be willing to walk point for him as secretary. She is also one of education’s highest-profile figures who isn’t afraid to push hard for what she wants. And she also created and for several years led StudentsFirst, a state-level advocacy group that backed choice and strong teacher and school accountability, for a few years.

So Rhee might have developed the political connections to be a welcome federal partner for states and districts as they work on transitioning to the Every Student Succeeds Act.

But Rhee hasn’t been particularly active in education policy since 2014, when she stepped down as the leader of StudentsFirst, which recently merged with fellow advocacy group 50CAN. She’s also married to Kevin Johnson, the Democratic mayor of Sacramento—so her husband’s party affiliation might not help her.

Photos: Michelle Rhee, former D.C. school chancellor and founder of education advocacy group StudentsFirst; Success Academies Charter Schools founder Eva Moskowitz during a charter school rally in 2015 in Albany, N.Y. (Mike Groll/AP-File)