This is a rush transcript from "Special Report with Bret Baier," October 5, 2018. This copy may not be in its final form and may be updated.

(BEGIN VIDEO CLIPS)

U.S. AMBASSADOR TO U.N. NIKKI HALEY: It has been an honor of a lifetime. You know, I said I'm such a lucky girl.

PRESIDENT DONALD TRUMP: Nikki Haley, ambassador to the United Nations, has been very special to me. She's done an incredible job. She's a fantastic person, very importantly, but she also has is somebody that gets it.

HALEY: I'm not leaving until the end of the year. My goal is that we make sure that everything is in a good place for the next ambassador to come in. I'm a believer in term limits. For all of you that are going to ask about 2020, no, I am not running for 2020.

TRUMP: Hopefully you will be coming back at some point, but maybe in a different capacity. You can have your pick.

(END VIDEO CLIPS)

BRET BAIER, ANCHOR: That is the rarest of events, a resigning cabinet member getting a real frontline sendoff in the Oval Office. Nikki Haley, the U.S. ambassador of the U.N., saying she will leave at the end of the year. It was a big surprise to a lot of people. Just in the past few minutes the president has told reporters aboard Air Force One that he has five people on a short list to replace her, among them Dina Powell who left as deputy national security adviser before. He said he wanted to bring her back at some time. He may have his opportunity now.

He says there are others on the list and he'll have a decision in the next couple of weeks. One of them tweeted that she does not have the job or want it, and that is his daughter, Ivanka Trump. "It's an honor to serve in in the White House alongside so many great colleagues, and I know that the president will nominate a formidable replacement for Ambassador Haley. That replacement will not be me." That was speculation through some of the day.

Let's bring in our panel: Steve Hilton is former adviser to British Prime Minister David Cameron and the host of "The Next Revolution" here on Fox News Channel; Susan Page, Washington bureau chief at USA Today; Jonathan Swan, national politics reporter for Axios who broke this story today, and Tucker Carlson, host of "Tucker Carlson Tonight" and the author of the new book, "Ship of Fools, How a Selfish Ruling Class is Bringing America to the Brink of Revolution." Apparently it's number one everywhere. You just trip over at the airports.

TUCKER CARLSON, FOX NEWS: I did today.

BAIER: First to Jonathan. You broke this story. It took a long time to figure out was there anything more to it, and it may be that there is not.

JONATHAN SWAN, AXIOS: I'm still trying to figure it out. Yes, I broke the story, but I still don't feel like I know what actually happened or why. I have been told numerous accounts of what happened and why, including it was long planned and everything is great and there is a beautiful ribbon around it, and maybe that's the case. I haven't reported anything so I just I don't have a high enough degree of confidence that anything I've been told so far is the actual truth.

BAIER: Tucker, what about this and what it means?

CARLSON: We'll find out in the end. Everything is revealed, nothing is hidden. Ultimately everyone I know believes there is a story there. Nobody knows what it is. The deeper question is why the president hired Nikki Haley in the first place. Very popular among a lot of Republican voters, she's impressively unintimidated, hyper-articulate, great on television, but she's articulated a foreign policy that is directly at odds with the one the president ran on, directly at odds, the same sort of 2002 neoconservatism that he attacked. And she continued in her position as U.N. ambassador to essentially contradict the president's own positions as he explained them, and brought us, I would say, closer to conflict with a bunch of different countries that he, again, ran against bringing us into conflict with.

And by the way, she was also one of his bitterest opponents in the primary. She compared him to Dylann Roof, the racist mass murderer. It does say something about his capacity for forgiveness, but I think most people I know who watched the administration full time were baffled by the misalignment between what she clearly believes and what he clearly believes. It doesn't make any sense.

BAIER: He gave her a pretty nice send-off.

CARLSON: If you are the White House, and everyone I have spoken to over there today said the same thing, you are concerned about her future political plans, or why she might say. And so you want to keep her close.

BAIER: Susan, it's also possible that this was her timing, and she decided that if the Republicans have any losses in the midterms that perhaps it would look like she was abandoning ships, and to do it now, she gets the Oval Office sendoff.

SUSAN PAGE, USA TODAY: That's right. And there is no suggestion that she's bailing because of the setbacks for the Republicans in the midterms. And I think that explanation makes some sense. Maybe we will find out something more complicated and conspiratorial is behind this, but it's possible that Nikki Haley wants to be president. I think that's pretty clear. That whatever benefit she is going to get out of being U.N. ambassador she's gotten in the space of about two years in all this, and that there's every reason to leave when she gets the Oval Office send-off, she gets a lot of positive press. The president embraces her. The praises the president's children.

SWAN: I think it's also, just to jump in, it's worth noting the stupidity of the theories going around, that there is this beautiful five-dimensional game of chess in which they have lined up a Lindsey Graham for Justice and she's going to be a senator. Anyone who has played glancing attention to the White House, there is no chessboard, there's no six moves ahead. Give me a break. It's absurd, just truly absurd.

PAGE: No chessboard for --

SWAN: And people who are otherwise intelligent people are saying this nonsense.

PAGE: But Nikki Haley could have some three steps ahead. She may be thinking this makes sense for her. I'm not saying she's running for the Senate. I'm saying maybe she does some kind of high profile --

SWAN: I'm sure she has a plan.

PAGE: But I agree it's not like there is a master White House --

SWAN: Yes.

BAIER: Steve?

STEVE HILTON, FOX NEWS HOST: All right, so let's look at the replacement. It seems to me that the effectiveness of the administration has really improved when the president has put in senior positions people who he gets on with it and respects and to a certain extent --

BAIER: Or has his ear.

HILTON: Like Pompeo, like Larry Kudlow. I think that's an improvement. And so I think in terms of the replacement he should definitely avoid another case of that Rex Tillersons, some establishment type that is highly recommended but doesn't really fit how he see things.

To Tucker's point earlier, I would also add there's something really interesting in his remarks today. When he was talking about North Korea and he was talking about building up the economy of North Korea, to me it was such a classic example of why he is different. The establishment politicians with an enemy, they send in tanks and soldiers. President Trump wants to send in entrepreneurs and investment. And he wants someone who shares that worldview, not, as Tucker said, someone who actually disagrees with it.

BAIER: He says he wants to move forward with this meeting with Kim Jong- un. Secretary Pompeo coming back from North Korea with glowing remarks about where they think it's going. What about that part of it?

CARLSON: This is actually what Trump ran on it, a wholesale rethinking of our foreign policy including with North Korea, averting war rather than marching relentlessly toward it. I think we are at about the 17th anniversary of the war in Afghanistan, and the president has said this out loud and anyone who has talked to people who work around him can confirm, he wants to get out and has been thwarted in that, this was detailed at length in Bob Woodward's book. He wants to get out and has been thwarted in that by his own foreign policy establishment, another reason that you want people around you who understand why you were elected.

BAIER: Is Dina Powell one of those people?

CARLSON: I can't assess that. I also can't overstate the degree to which the people around the president are afraid of Nikki Haley. And I'm not endorsing this view, I'm not Nikki Haley's, some of them think that she is politically treacherous, not a bad person, but that she has a very distinct agenda that is not the president's at all, and they're worried what she might do.

BAIER: We should also point out that in this foreign policy establishment there was the rocky Secretary Tillerson time, but then there was Pompeo who took off and has the ear of the president. And obviously John Bolton has a lot of U.N. experience as a former U.S. ambassador to the U.N. and probably has a more active role there, too.

PAGE: That's right. So the very high-profile she has had previously before -- with the previous, the initial team with McMaster and with Tillerson, it is probably going to be a little more constrained now with the new team that is more confident of itself, that has President Trump's ear. And that may be also part of her calculation, that that was one reason it was time to move because her influence might have been constrained compared with where it was before.

BAIER: Last word?

SWAN: I just think that we still don't know what happened, which is remarkable in this White House. Usually you know in real time with all this stuff. And the fact that it didn't leak out is also remarkable. Mike Pompeo was taken by surprise, and so were quite a number of people at the senior level.

BAIER: And I heard some commentators today saying, why would they do this and take away from the Kavanaugh momentum that they had? There are 7 billion new cycles before the midterms.

(LAUGHTER)

HILTON: Exactly. He'll find ways of keeping this story going, you can be sure of that.

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