Michael Bloomberg as Secretary of State in a Clinton presidency?

Michael Bloomberg wants to be Hillary Clinton's secretary of State.

That's according to the latest batch of Mrs. Clinton's leaked emails, revealed Saturday in a WikiLeaks hack. Political observers have honed in on one particular email exchange from June 2015 in which a Clinton contact, after confirming with a Bloomberg aide that the former New York City mayor wasn't really considering running for president, asked what position Mr. Bloomberg would like in a Clinton administration.

"Is there something Mike Bloomberg would want to do in his life in an Admin?" a Clinton ally allegedly wrote. "Is like Ambassador to China way too small?"

"Secty of state Which ain't gonna happen," the Bloomberg aide responded.

The aide is probably correct: Bloomberg, who vigorously supported Clinton's campaign and called Donald Trump "a dangerous demagogue" at the Democratic National Convention, probably won't be asked to serve that coveted role. The billionaire rarely comes up in cabinet predictions, and some analysts say that he doesn't have the foreign policy chops for the position.

Nonetheless, the revealed exchange renewed attention on a potential Clinton cabinet, what she's likely to consider when in forming it, and who might serve in a Clinton administration, if she wins the election.

"The cabinet is a clear sign of the governing priorities of a president," says John Baick, a professor of history at Western New England University in Springfield, Mass. "Some cabinets have exercised very little power, with membership designed for optics rather than leadership. And some cabinets have been a reflection of internecine war, either within the White House or the party. Look for Clinton, if she wins, to follow the kind of pattern of President Obama, President Clinton, or President George H.W. Bush."

Of course, the Democratic nominee hasn't revealed much publicly about her Cabinet picks. In April, she famously said she'll "have a cabinet that looks like America, and 50 percent of America is women," a pledge that may place a strain on a Democratic establishment that is predominantly male, says Professor Baick. Clinton also said she would consider tech leaders for top posts. And political observers predict she'll prioritize diversity – we may see the first LGBT cabinet secretary – as well as "loyalty, as that has loomed large for her," says Nick Clark, a professor of political science at Susquehanna University in Selinsgrove, Penn.

Her vice presidential pick may offer clues as to what she will look for in cabinet secretaries, says Baick.

"Clinton has already set the tone for her Cabinet with her selection of Tim Kaine. Experienced, steady, loyal, and on message will be the kind of qualities that the Clinton transition team will emphasize if Secretary Clinton is elected," he says. "Do not expect any surprises or dark horses."

Cabinet choices are considered important because "the federal bureaucracy is so large, unwieldy, and independent-minded that it presents an almost insurmountable obstacle to a president who hopes to move it at all in her policy direction," says David Ryden, a professor of political science at Hope College in Michigan. "The secretaries of the key departments ... are critically important appointments to a president's ability to pursue her policy priorities in [those areas]." 

One person who won't be in a possible future Clinton cabinet: Bill Clinton. The former president said he asked to be put in charge of helping to revitalize the economy.

"I have asked, actually, to be given the job of trying to help every part of the United States that has been left out and left behind economically," Bill Clinton said while campaigning for his wife in Puerto Rico in May.

But an 1967 anti-nepotism statute would preclude a cabinet position for Bill Clinton, who would more likely serve as an informal adviser.

Who might serve in a potential Clinton cabinet? Here's a look at several top spots and contenders:

Secretary of State: This is the most coveted and most-watched seat, and even more so now because it's also Clinton's former position. While current Secretary of State John Kerry is probably eager to stay on board, it's likely Clinton will appoint her own pick like Wendy Sherman, the former undersecretary of state for political affairs and a key player in the Iran nuclear deal, or Bill Burns, a career diplomat who was also deputy secretary of state.

Chief of staff: Most political observers see this as a shoo-in for Cheryl Mills, Clinton’s chief of staff at the State Department. Politico calls her "one of the smartest and most trusted people in Clinton’s orbit," and if appointed, she would be the first female White House chief of staff, as well as the first African-American. Obama's secretary of agriculture and former Iowa Gov. Tom Vilsack may be a dark horse contender.

National security adviser: Jake Sullivan, who worked for Clinton at the State Department, as national security adviser to Vice President Joe Biden, is often seen as the most likely contender.

Defense secretary: Former Undersecretary of Defense for Policy Michèle Flournoy is seen as the most likely choice, and would be the first woman in the position. But she declined the position in 2014 when President Obama offered, citing her family. It's unclear whether she would do the same under a potential Clinton administration.

Treasury secretary: Political observers have their eyes on who Clinton will tap to fill this position. Bernie Sanders supporters and progressives are watching to see if Clinton will uphold her commitment to progressive economics. Appointing Sen. Elizabeth Warren (D-Mass.) would thrill progressives – and anger Republicans. Another possibility is Sheryl Sandberg, a former Treasury official who's currently the chief operating officer at Facebook. If nominated, either would be the first female Treasury secretary.