Politico (Hadas Gold) includes a video that shows Donald Trump (at a Fort Worth rally) saying:
I’m going to open up our libel laws so when they write purposely negative and horrible and false articles, we can sue them and win lots of money. We’re going to open up those libel laws. So that when The New York Times writes a hit piece which is a total disgrace or when the Washington Post, which is there for other reasons, writes a hit piece, we can sue them and win money instead of having no chance of winning because they’re totally protected. You see, with me they’re not protected, because I’m not like other people, but I’m not taking money — I’m not taking their money. So we’re going to open up those libel laws, folks, and we’re going to have people sue you like you never got sued before.
Politico also says (though this appears to be from before the start of their video) that Trump was saying that this was “One of the things I’m going to do if I win.”
Of course, if a plaintiff can show that an article is false, and the authors know it’s false (or know it’s likely false), then he can already win under libel law. But if not (and if the plaintiff is a public figure and the article is on a matter of public concern), then the Supreme Court’s decision in New York Times Co. v. Sullivan (1964) precludes that; even if Trump is elected President, he can’t change that (unless he appoints enough Justices and uses their views on reversing Sullivan as a litmus test).
More broadly, libel law is almost exclusively state law. Even apart from the First Amendment, and even assuming that Trump is implicitly saying that he’d get a cooperative Congress to change the law, he must be contemplating a sharp increase in federal authority here. That is, of course, if he’s actually serious.