President Obama has quietly promised Massachusetts Sen. Elizabeth Warren complete support if she runs for president — a stinging rebuke to his nemesis Hillary Clinton, sources tell me.

Publicly, Obama has remained noncommittal on the 2016 race, but privately he worries that Clinton would undo and undermine many of his policies. There’s also a personal animosity, especially with Bill Clinton, that dates from their tough race six years ago.

A former Harvard law professor and administration aide, Warren would energize the left wing of the Democratic Party just as Obama did against Clinton in 2008.

Thanks to her outspoken stand against big banks and the top 1 percent, Warren is the darling of progressives. She won her Senate seat thanks to millions of dollars in donations from outside Massachusetts, including from rich environmentalists and Hollywood celebrities.

Obama has authorized his chief political adviser, Valerie Jarrett, to conduct a full-court press to convince Warren to throw her hat into the ring.

In the past several weeks, Jarrett has held a series of secret meetings with Warren. During these meetings, Jarrett has explained to Warren that Obama is worried that if Hillary succeeds him in the White House, she will undo many of his policies.

He believes that the populist Warren is the best person to convince the party faithful that Hillary is out of touch with poor Americans and the middle class. Warren, in his view, would carry on the Obama legacy after he leaves the White House.

So far, Warren has been reluctant to make a commitment. During several recent interviews, she has said she has no present plans to run for president.

However, she always phrases her stance on the issue in the present tense and has refused to issue a Shermanesque statement that she will not run for the White House under any circumstances.

“Barack, Michelle and Valerie have been talking about Elizabeth Warren for quite some time,” says an Obama administration source. “Valerie has told Warren that Obama is prepared to throw a great deal of money and organizational support behind her.

“The Obamas believe that Warren sees things from the same ideological point of view as they do. She is a committed progressive who, like Obama, wants to transform America into a European-style democratic-socialist state.”

Bill Clinton has worried for some time about Obama backing another candidate, as I revealed in my book “Blood Feud.”

“I’ve heard from [Democratic] state committeemen about Obama’s preference in ’16,” Bill confided to several of his close friends. “And they tell me that he’s looking around for a candidate who’s just like him. Someone relatively unknown. Someone with a fresh face. He wants to clone himself — to find his Mini-Me.”

When I ran this information before a well-informed Democratic Party operative, he pooh-poohed the scenario.

“It’s all bulls–t,” he said. “The media is creating a Hillary Clinton-Elizabeth Warren rivalry to hype the storyline. If Warren dared to challenge Hillary, women all over America would never forgive her. She’d lose all her credibility.”

That, however, is not the way Valerie Jarrett sees things.

“Both Valerie and Michelle Obama have convinced the president that Elizabeth Warren is his Mini-Me,” said a person who has discussed the issue with Jarrett.

This person continued: “For the time being, the Obamas have decided not to broadcast the fact that they’ve tapped Warren as their chosen candidate. They are waiting until the moment is right, which will probably be after the midterm elections.”

Edward Klein is the author of “Blood Feud: The Clintons vs. the Obamas” (Regnery Publishing), which debuted this weekend at No. 1 on The New York Times best-seller list.