In his new book, “Blood Feud,” journalist Edward Klein gets inside the dysfunctional, jealous relationship between Bill and Hillary Clinton and Barack and Michelle Obama — and how it could explode in 2016.

Outwardly, they put on a show of unity — but privately, the Obamas and Clintons, the two power couples of the Democratic Party, loathe each other.

“I hate that man Obama more than any man I’ve ever met, more than any man who ever lived,” Bill Clinton said to friends on one occasion, adding he would never forgive Obama for suggesting he was a racist during the 2008 campaign.

The feeling is mutual. Obama made ­excuses not to talk to Bill, while the first lady privately sniped about Hillary.

On most evenings, Michelle Obama and her trusted adviser, Valerie Jarrett, met in a quiet corner of the White House residence. They’d usually open a bottle of Chardonnay, catch up on news about Sasha and Malia, and gossip about people who gave them heartburn.

Their favorite bête noire was Hillary Clinton, whom they nicknamed “Hildebeest,” after the menacing and shaggy-maned gnu that roams the Serengeti.

‘Michelle could be president’

The animosity came to a head in the run-up to the 2012 election, when Obama’s inner circle insisted he needed the former president’s support to win. Obama finally telephoned Bill Clinton in September 2011 and invited him out for a round of golf.

“I’m not going to enjoy this,” Bill told Hillary when they gathered with a group of friends and political associates at Whitehaven, their neo-Georgian home on Embassy Row in Washington, DC.

“I’ve had two successors since I left the White House — Bush and Obama — and I’ve heard more from Bush, asking for my advice, than I’ve heard from Obama. I have no relationship with the president — none whatsoever,” Clinton said.

“I really can’t stand the way Obama ­always seems to be hectoring when he talks to me,” Clinton added, according to someone who was present at the gathering and spoke on the condition of anonymity. “Sometimes we just stare at each other. It’s pretty damn awkward. Now we both have favors to ask each other, and it’s going to be very unpleasant. But I’ve got to get this guy to owe me and to be on our side.”

During the golf game, Clinton didn’t waste any time reminding Obama that as president, he had presided over eight years of prosperity, while Obama had been unable to dig the country out of the longest financial ­doldrums since the Great Depression.

“Bill got into it right away,” said a Clinton family friend. “He told Obama, ‘Hillary and I are gearing up for a run in 2016.’ He said Hillary would be ‘the most qualified, most experienced candidate, perhaps in history.’ His reference to Hillary’s experience made Obama wince, since it was clearly a shot at his lack of experience when he ran for president.

“And so Bill continued to talk about Hillary’s qualifications . . . and the coming campaign in 2016. But Barack didn’t bite. He changed the subject several times. Then suddenly, Barack said something that took Bill by complete surprise. He said, ‘You know, Michelle would make a great presidential candidate, too.’

“Bill was speechless. Was Barack comparing Michelle’s qualifications to Hillary’s? Bill said that if he hadn’t been on a mission to strike a deal with Barack, he might have stormed off the golf course then and there.”

BlackBerry snub

Bill Clinton would go on to campaign for Obama in 2012, but he felt betrayed when the president seemed to waver when it came to a 2016 endorsement of Hillary. Obama attempted to smooth things over with a joint “60 Minutes” interview with Hillary, and later a private dinner for the two couples at the White House.

I hate that man Obama more than any man I’ve ever met, more than any man who ever lived. - Bill Clinton in 'Blood Feud'

And so, on March 1, 2013 — the very day that the $85 billion in budget cuts known as the “sequester” went into effect — the Clintons slipped unnoticed into the White House and sat down for dinner with the Obamas in the Residence.

Typically, once Obama decided to do something (for example, the surge in Afghanistan), he immediately had second thoughts, and his behavior during dinner degenerated from moody to grumpy to bad-tempered.

After the obligatory greetings and small talk about family, Obama asked Bill what he thought about the sequester: Would it turn out to be a political plus for him? Bill went into a long — and boring — lecture about the issue.

To change the subject, Hillary asked Michelle if it was true, as she had heard, that the first lady was thinking about running for the Senate from Illinois.

Michelle said that she was warming to the idea, though she had yet to make up her mind.

Bill shot Hillary a look of incredulity.

Bill then moved the conversation to Obama’s vaunted 2012 campaign ­organization. He told Obama that it would be a good idea to fold the organization, along with all its digital and social-media bells and whistles, into the Democratic National Committee.

Obama’s only response was a disparaging smile.

“You have to use your organization to aid the candidate in 2016,” Bill pressed Obama.

“Really?” Obama replied in a tone of undisguised sarcasm.

The two men went back and forth over the subject of where the money for Obama’s campaign organization had come from and how to allocate funds for the 2016 presidential election. Bill raised his voice. So did Obama.

As Bill Clinton went on about his managerial experience, Obama began playing with his BlackBerry under the table, making it plain that he wasn’t paying attention to anything Clinton had to say. He was intentionally snubbing Clinton. Others around the table noticed Obama thumbing his BlackBerry, and the atmosphere turned even colder than before.

Hillary changed the subject again.

“Are you glad you won’t have to campaign again?” she asked Obama. “You don’t seem to ­enjoy it.”

“For a guy who doesn’t like it,” Obama replied tartly, “I’ve done pretty well.”

“Well,” Bill said, adding his two cents, “I was glad to pitch in and help get you re-elected.”

There was another long pause. Finally, Obama turned to Bill and said, sotto voce, “Thanks.”

After the dinner, and once the Clintons had been ushered out of the family quarters, Obama shook his head and said, “That’s why I never invite that guy over.”

Obama’s Mini-Me

Lately, Bill Clinton has become convinced that Obama won’t endorse Hillary in 2016. During a gathering at Whitehaven, guests overheard Bill talking to his daughter, Chelsea, about whether the president would back Joe Biden.

“Recently, I’ve been hearing a different scenario from state committeemen,” Clinton said. “They say he’s looking for a candidate who’s just like him. Someone relatively unknown. Someone with a fresh face.

“He’s convinced himself he’s been a brilliant president, and wants to clone himself — to find his Mini-Me.

“He’s hunting for someone to succeed him, and he believes the American people don’t want to vote for someone who’s been around for a long time. He thinks that your mother and I are what he calls ‘so 20th century.’ He’s looking for ­another Barack Obama.”

Excerpted from “Blood Feud: The Clintons vs. the Obamas” by Edward Klein, out this week from Regnery Publishing.