(CNN) Before President Donald Trump reportedly asked then-FBI Director James Comey to end the investigation into deposed national security adviser Michael Flynn 's ties to Russia, he also reportedly made a remarkable suggestion about journalists.

"Alone in the Oval Office, Mr. Trump began the discussion by condemning leaks to the news media, saying that Mr. Comey should consider putting reporters in prison for publishing classified information, according to one of Mr. Comey's associates."

Um, what?

Understandably, the bulk of the coverage in the wake of Schmidt's bombshell has focused on what it means for Trump if he did indeed ask Comey to stop an ongoing investigation. (White House press secretary Sean Spicer said Wednesday afternoon of the reported meeting: "The President's been very clear. This is not an accurate representation of that meeting.")

But, the suggestion from a sitting President of the United States to the FBI Director that journalists be jailed for reporting on classified information is, in and of itself, a stunning statement that goes beyond even Trump's most virulent anti-media statements to date.

Throughout the 2016 campaign and even in the White House, Trump has been outspoken about his distaste for the media. He would regularly refer to the journalists covering the campaign as "some of the most dishonest people" he had ever met and insist that the press was deeply biased against him.

Even as recently as Wednesday, at a commencement speech at the Coast Guard Academy, Trump, ripped the media for its alleged bad treatment

"Look at the way I have been treated lately, especially by the media," Trump told the graduates. "No politician in history, and I say this with great surety, has been treated worse or more unfairly. You can't let them get you down, you can't let the critics and the naysayers get in the way of your dreams."

And, his administration hasn't been shy about its desire to crack down on the leaking of classified information.

Trump has repeatedly insisted that the leaks coming from the intelligence community are the real story regarding Flynn and the Russia investigation. In March, he tweeted : "The real story that Congress, the FBI and all others should be looking into is the leaking of Classified information. Must find leaker now!" And in February he said this ( via Twitter , again): "The real scandal here is that classified information is illegally given out by "intelligence" like candy. Very un-American!"

It's worth noting here that no president was harder on leakers than the man who preceded Trump in the White House. Then-President Barack Obama set records for the number of leak prosecutions. Obama defended that record as the result of a number of holdover prosecutions from the George W. Bush White House.

"Many of the cases that are often lumped into, you know, my ledger, essentially were cases that were brought before we came into office," he said in an interview with the Rutgers University student newspaper last year . "Some of them are serious, where you had purposeful leaks of information that could harm or threaten operations or individuals who were in the field involved with really sensitive national security issues."

Still, what we are talking about here is not prosecuting leakers but rather the journalists who are on the receiving end of those leaks. And that is something entirely different -- and more dangerous.

"He's had a running war with the media but this, if this were actually to happen, would be a very dark new chapter," CNN media reporter Brian Stelter said on CNN's "New Day Wednesday morning

It seems extremely unlikely that Trump or whomever he appoints as his next FBI director would put much emphasis on the jailing of journalists who report on classified information. And there is a widespread belief in the journalistic (and legal) community that such an effort would be doomed to failure. (Side bar: This Congressional Research Service report from February 2017 suggests it is a bit more of an open question.)

The point is not that this will happen anytime soon -- or, hopefully, ever. The point is that the president of the United States reportedly floated the idea of jailing journalists for reporting classified information in a one-on-one exchange with the then director of the FBI.

Sit with that for a little while.