WASHINGTON — A fight between the White House and State Department has broken out over ambassadorships after chief of staff Reince Priebus tried to circumvent Secretary of State Rex Tillerson to hand out the coveted posts to GOP loyalists, sources told The Post.

“Tillerson had a deal that if he were to come on board, he would have a decision on who the ambassadors were going to be,” a transition source said.

“The process was supposed to be where transition was going to give two names for each position and Tillerson was going to interview those people for each country — and Tillerson would make the decision,” the source explained.

But Priebus is using his Oval Office access to get President Trump to sign off on a list of some of the most desirable diplomatic postings, angering State Department officials, multiple sources confirmed.

So far, Priebus has pushed — and won signoffs — for Miami Marlins owner Jeff Loria to head to France, GOP activist Georgette Mosbacher to Luxembourg, financier Lew Eisenberg to Italy and hedge funder Duke Buchan to Spain.

The list has led some at the State Department to worry that Priebus has not properly vetted the diplomats-to-be.

“The people Reince has put up are problematic as well,” said a State Department official.

“Eventually, what Reince is doing has to be squared with process and reality. I’m not sure the White House is exactly stoked about this as they dig deeper into the background of these people,” he added.

In a joint statement, Tillerson and Priebus denied any rift.

“We have a very close relationship and speak often. We have a great system in place to assure mutual agreement on all Ambassadorships.”

Eisenberg, a Republican National Committee loyalist who helped lead the effort to raise funds for Trump’s presidential campaign, was pushed out of Goldman Sachs after a sexual harassment accusation — an issue that would surely come up at a confirmation hearing. (His accuser reportedly recanted her claims.)

Buchan, who donated to a super PAC supportive of Jeb Bush and then Marco Rubio before finally coming around to Trump, was an owner of a company, NewCastle Investment Corp., that in 2009 sued Trump.

“Mr. Buchan’s investment fund previously owned shares of Newcastle, but does not currently and was never a part of company management or its board,” Kevin Madden, a spokesman for the hedge funder, said.

But Buchan also has Cayman Island funds and faces other financial issues that could make his confirmation contentious.

In addition to Nikki Haley to the UN, the Trump administration has officially only nominated two ambassadors — David Friedman for Israel and Terry Branstad to China.

The president has also signaled that he intends to select businessman William Hagerty to be ambassador to Japan and Jets owner Woody Johnson to the UK.