Secretary of State Bloomberg? It’s not unthinkable.

A confidant of Mike Bloomberg floated to a top Hillary Clinton adviser the idea of giving the former mayor the Cabinet post, according to a batch of e-mails released Saturday by WikiLeaks.

Clinton aide Neera Tanden asked Howard Wolfson — a current Bloomberg consultant and former deputy mayor — in a June 3, 2015, e-mail whether the former mayor was seriously considering a run for president.

Tanden had spotted a tweet by top Bloomberg strategist Kevin Sheekey citing a June 2 Post column by Michael Goodwin that revealed that New York Democrats had approached Bloomberg to challenge Clinton.

“What is up?” Tanden asked Wolfson, who worked as Clinton’s spokesman during her 2008 presidential bid.

The message was sent eight minutes after Sheekey’s tweet linking to Goodwin’s column was posted.

Wolfson, who hosted a fundraiser for Clinton in May, sought to reassure Tanden that Bloomberg didn’t seek to challenge the former first lady.

“I find the whole thing laughable,” he responded.

“Ok good I was worried you were losing it,” Tanden replied.

She then asked what Bloomberg would want to do in a Clinton administration.

Tanden floated an ambassadorship to China but worried it might be “way too small” for the media magnate, her e-mail said.

Wolfson countered with a bigger title: secretary of state, but mused that it “ain’t gonna happen.”

But the Clinton camp was dead serious about the exchange and Bloomberg’s ambitions. The entire e-mail chain was forwarded by Tanden to Clinton campaign chairman John Podesta.

She added the note, “Something to know for down the road.”

Wolfson backed off his earlier e-mails, telling The Post on Saturday that the only job in politics that interested Bloomberg was the presidency.

“I think Mike made it pretty clear that the job he wanted was the top job,” Wolfson said.

Bloomberg thinks Henry Kissinger would make a good choice for secretary of state, Wolfson added.

The three-term mayor has lusted after the White House since 2006 and came closest to launching a bid in January when he asked his advisers to analyze the viability of an independent run.

But Bloomberg backed down two months later, saying in an announcement, “If I entered the race, I could not win.”

Clinton reached out to Bloomberg shortly after his decision, according to a March 11, 2016, e-mail from Clinton aide Huma Abedin to Podesta, which WikiLeaks released Saturday.

The Democratic presidential nominee has revealed little about who she would stuff in her Cabinet, saying only that she would fill half the positions with women and consider tech leaders for posts.

The e-mails released Saturday contained thousands of communiques between top aides, including excerpts from Clinton’s speeches to Wall Street banks, discussions on how to defend the former secretary of state’s use of a private e-mail server, and early plans to lay the groundwork of her 2016 run.

In one e-mail chain, Clinton aides whined that the press was not taking the Democratic nominee’s apologies for using a private server seriously.

“Everyone wants her to apologize. And she should. Apologies are like her Achilles heel,” Tanden said in a September 2015 e-mail to Podesta.

Podesta, in a August 2015 e-mail to Clinton, urged her to “bury the hatchet” with former New Mexico Gov. Bill Richardson even though he endorsed Barack Obama over Clinton in 2008 and “can be a d- -k.”

Clinton’s campaign Saturday did not address the veracity of the e-mails WikiLeaks has released, but blamed the Russian government for the hack and compared the cyberspying to the Watergate break-in.