American Media Inc. is trying to sell the National Enquirer, its most famous publication. The question remains: Who wants to buy it, and what, exactly, is AMI selling?

In a statement late Wednesday, the company’s board confirmed a Washington Post report that it is “exploring strategic options” for the Enquirer and two other tabloids, “which will likely result in their sale in the near future.”

On Thursday morning, the New York Times reported that representatives of the Enquirer were “deep in their negotiations” with billionaire Ron Burkle, who made his fortune as a supermarket magnate and is a longtime donor to Democratic political causes. He and former president Bill Clinton are friends, leading to inevitable questions about the Enquirer’s close relationship with President Trump and Burkle’s possible political motivations in buying the tabloid.

Two sources with knowledge of the discussions confirmed to The Post that Burkle and the Enquirer had been talking about a possible deal.

But soon after, Frank Quintero, a spokesman at Burkle’s investment firm, Yucaipa, denied those reports. “We’re not interested in pursuing the National Enquirer,” Quintero told The Post.

American Media CEO David Pecker and Burkle, who were partners in the now shuttered Radar Magazine and, have spoken once in the wake of the Enquirer’s announcement, said a person close to the discussions who spoke on the condition of anonymity because that person was not authorized to speak about them publicly. In that discussion, Burkle expressed his displeasure that his name is being bandied about as a possible buyer, the person added.

However, AMI spokesman Jon Hammond said Burkle and Pecker have not spoken, and he declined to comment on discussions regarding the tabloid’s sale.

“Pecker and Burkle have a preexisting relationship,” said another person speaking on the condition of anonymity who is familiar with the negotiations but is not authorized to speak about them openly. “Burkle isn’t involved with Trump or anything like that. He’s not in this for the politics. He’s out to make a buck.”

Burkle has expressed interest in buying media properties in the past, including the Wall Street Journal and Knight-Ridder newspapers. He did not make an offer for either property.

In 2006, the press-shy Burkle accused a New York Post columnist of trying to shake him down for hundreds of thousands of dollars in exchange for not writing about his personal life. In 2002, he told federal investigators that the Hollywood private detective Anthony Pellicano also demanded payment in exchange for Pellicano not investigating him.

The Enquirer’s stories during the 2016 presidential election — lauding Trump’s candidacy and attacking his rivals — flew mostly under the radar of mainstream outlets and rose to prominence largely through Trump’s mentions of them on the campaign trail.

But the Enquirer is also known for the information that it holds but has not printed. The Enquirer keeps a safe in its offices — where a person familiar with its content said it has held information about celebrities, including Trump, Charlie Sheen and Tiger Woods.

The “catch-and-kill” agreement between the tabloid and former Playboy model Karen McDougal, whom the Enquirer paid to keep quiet about her alleged longtime affair with Trump, was also kept in the safe.

Any potential buyer of the Enquirer would presumably also acquire all the tabloid’s reporting material, as well as its archive, which contains famous images such as Elvis Pressley’s corpse in his coffin, among others.

The tabloid’s “catch and kill” tactics, in which a source is paid for exclusive rights to a story but the article is never published, landed the company, Pecker, and AMI’s chief content officer, Dylan Howard, in legal jeopardy. The two men were close to being indicted when they worked out a non-prosecution agreement with federal investigators looking into their efforts to tilt the election for Trump.

But that heat appears to have been too much for AMI’s board, which began discussing whether it should unload the paper in August, just as the non-prosecution agreements were being finalized. One person briefed on the board discussions told The Post that the board had those discussions because it “didn’t want to deal with hassles like this anymore.”

Two of AMI’s board members work for Chatham Asset Management, which is run by Anthony Melchiorre and which controls 80 percent of AMI. The other two members of the board are Pecker and a former Trump Casinos executive. While Melchiorre himself does not sit in the board meetings, he made his presence felt through his two representatives.

Melchiorre, who has dined with Trump alongside Pecker, was disconcerted by the reports of the Enquirer’s illegal election interference. But he was “disgusted” by the tabloid’s reporting on the extramarital affair of Jeff Bezos, who accused AMI of extortion and blackmail, according to a person familiar with the internal deliberations over the AMI sale.