Carly Fiorina is in the running to be America’s top spy, according to a report.

The former Republican presidential candidate visited Trump Tower on Monday for a job “interview” to be director of national intelligence, the New York Times reported Monday.

Trump aides had discussed Fiorina as a possible secretary of state pick, a transition source said. But reports suggest the president-elect has instead settled on Exxon Mobil CEO Rex Tillerson for that job.

The once-fierce Trump opponent emerged from her meeting with only praise for the president-elect.

“First I want to say, he has really cool stuff in his office,” she told reporters waiting near the elevator bank in Trump Tower. “I was particular taken by a Shaq O’Neal shoe, which is huge. I guess it takes a champion to know a champion.”

She also addressed election-related hacks, which intelligence agencies have blamed on the Russians.

“[We] spent a fair amount of time talking about China as probably our most important adversary and a rising adversary. We talked about hacking, whether it’s Chinese hacking or reported Russian hacking,” she said, raising the specter that Team Trump believes the election hacks were carried out by the Chinese, not the Russians.

In an email to The Post, Fiorina’s chief of staff described the powwow like this: “It was a positive and productive meeting. Carly and the President-Elect discussed issues ranging from America’s strategic interests and national security challenges abroad to the geopolitical climate across the world and in China.”

Fiorina, who was in the field running against Trump for the Republican presidential nomination, would come to the DNI job with some experience. The former Hewlett-Packard CEO was chair of the CIA’s external advisory board, and after 9/11 worked with the NSA and Department of Defense.

But she also sparred with the president-elect during the campaign. “Look at that face!” Trump said of Fiorina during the primary contest. “Would anyone vote for that? Can you imagine that, the face of our next president?!”

At a primary debate the following week, Fiorina responded by saying, “I think women all over this country heard very clearly what Mr. Trump said.”

“I think she’s got a beautiful face and I think she’s a beautiful woman,” Trump said in return.

Later, after exiting the race as her support faded, Fiorina suddenly rejoined the fray by agreeing to be Sen. Ted Cruz’s vice presidential running mate. But the desperate attempt by Cruz to reignite his campaign fell flat and the duo exited the race for good shortly thereafter.

In September, just two months before the election, however, Fiorina finally endorsed the eventual winner. “We must have President Trump,” she told a Washington state Republican dinner on Sept. 8, 2016. “We can’t have President Clinton.”

Fiorina’s surprising return as a top official in the Trump administration could unite establishment Republicans around his presidency.

“Carly’s national security experience and business background would make her a fierce advocate for America’s interests abroad and could make her a consensus pick among Republicans,” said a top GOP source familiar with Fiorina.

On Monday, she praised Trump for bringing top talent into the administration. “The high quality of people that he’s named already says so much about his executive abilities,” she told reporters at Trump Tower.

The Trump transition team did not return a request for comment.