"I think it's something that we've looked at and how that gets executed or whether that goes anywhere is a different story," Priebus said to ABC News' Chief White House Correspondent Jonathan Karl on "This Week," Sunday.
"I think that newspapers and news agencies need to be more responsible with how they report the news," he said.
How could the libel laws change?
The only way to change the libel law is to "get courts to reinterpret that body of law or alter the U.S. Constitution," said Robert Corn-Revere, a First Amendment expert and attorney with Davis Wright Tremaine, LLP.
Amy Adler, a law professor at the NYU School of Law, said that such a move would have to come from growing dissent, which does not appear to be present, at least not right now.
"Constitutional lines are very clear and there is a shared consensus on the right and the left," she added. "This is not a divided issue."
A Constitutional amendment would require a Congressional vote and ratification from the states. The most recent proposal to alter the First Amendment was a movement to ban flag desecration that failed for the fourth time in 2005, according to Corn-Revere.
"He just can’t be serious," said Corn-Revere about Trump’s suggestions about changing libel law. "I can’t picture this gaining a lot of support."
What Trump has said about the libel laws in the past
Priebus may have been the one confirming the Trump administration's interest in reviewing libel laws this weekend, but Trump himself has questioned them openly in the past.
"They write false stories, you can't really sue because the libel laws are essentially non-existent," Trump said at an event in Arkansas in February 2016. "We're going to open up the libel laws so when they write falsely we can sue the media and we can get these stories corrected and get damages."
"For the most part I think libel laws almost don’t exist in this country," Trump said in The Washington Post meeting.
"I just think that if a paper writes something wrong," he said. "They should at least try to get it right. And if they don’t do a retraction, they should, they should you know have a form of a trial. I don’t want to impede free press, by the way. The last thing I would want to do is that."
In a meeting with New York Times executives and reporters on Nov. 22, 2016, the then-President-elect appeared to calm nerves about his earlier threats to reform libel laws.
"I think you’ll be happy," Trump said in the meeting, according to the transcript the paper published. "Actually, somebody said to me on that, they said, ‘You know, it’s a great idea, softening up those laws, but you may get sued a lot more.’ I said, ‘You know, you’re right, I never thought about that.’ I said, ‘You know, I have to start thinking about that.’ So, I, I think you’ll be O.K. I think you’re going to be fine."
His attitude appears to have changed in the subsequent months, however, tweeting in March "The failing @nytimes has disgraced the media world. Gotten me wrong for two solid years. Change libel laws?"