Kathy Griffin’s 24th stand-up tour, “Like A Boss,” comes to the Kennedy Center on Saturday, June 20. (Tyler Shields)

Celebrity-obsessed comedian Kathy Griffin has won two Emmys (in 2007 and 2008) for her reality show “My Life on the D List.” Last year, she took home a Grammy for the album “Calm Down Gurrl.” This week, her 24th stand-up tour, “Like A Boss,” comes to the Kennedy Center, where, the 54-year-old promises, she’ll be “well-prepped to talk about anything and everything.”

But there was one thing her handlers warned she would not address in interviews: Her short-lived stint earlier this year as a replacement for the late Joan Rivers on “Fashion Police.”

In a statement at the time, Griffin said the show wasn’t a good fit, adding: “Thank you to my fans for taking this ride with me. See you at the gay bars . . . and the MF-ing KENNEDY CENTER.”

The venue is clearly important to her. Indeed, she named a 2013 comedy special, taped in Minneapolis, “Kennedie Center On-Hers.”

Griffin spoke by phone from California, giddy about the news of the day: the Vanity Fair cover of Caitlyn Jenner. The conversation has been edited for space, but not necessarily for taste.

Kathy Griffin. (Courtesy Kennedy Center)

How are you?

I feel very Caitlyn right now. It’s all about Caitlyn.

I was going to try and leave Caitlyn out of this, but I guess there’s no avoiding it, huh?

You can’t keep Caitlyn out of it. The transes will come after you, guns a-blazin’. First of all, I call her Caitie. I call her Caitie because we’re destined to become besties. I actually love that Caitlyn is doing what she’s doing at the age of 65. I love that Cher is the face of Marc Jacobs at 68. All that stuff is great. Think about it: I could actually be onstage at the Kennedy Center when the decision comes down about the legalization of gay marriage. It could not be a better time to be in D.C. at the Kennedy Center.

Have you played the Kennedy Center before?

I have, and it is heaven. First of all, the acoustics are so perfect. You’d think that wouldn’t matter to a comic, but it does. The Kennedy Center audience is notoriously smart and open-minded and diverse. I’m going to have my vets there, and I’m going to have my soccer moms, and I’m going to have my LGBTQIA2s — I keep up with all the letters and numbers — and I’m going to have my married couples, my unmarried couples. That’s the great thing about the Kennedy Center: You get audience members who are coming because they have a subscription, or you get people because they’ve been following my social media, and they know that a couple of nights ago I went to see Lady Gaga and Tony Bennett at the Hollywood Bowl, and Lady Gaga gave me a box filled with eggs from her own chickens, so . . . .

What’s going to hatch out of those eggs? It might not be what you think.

I don’t care. Whatever hatches was “born this way.” It was so incredible. If I can tell you what it was like to be in an elevator two nights ago with Tony Bennett and his wife, and Gaga and her bodyguard: I was with my boyfriend, who is 17 years younger — and don’t even start with me on that. I’m in no mood. Life is short. Grab joy when you can. So I’m in an elevator and it’s just us, and everywhere I go, I’m looking for the funny. And there isn’t much happening. Then Lady Gaga pulls out a box, and hands it to Tony Bennett and explains, “These are from my own chickens, and Kathy, I brought some for you.” I said, you know what, that is a story. I’m going to go into more detail about this at the Kennedy Center. I said thank you for the eggs — and the material.

I was going to ask how you can come up with new material each year. Is it because there’s no end to the celebrities doing things like that?

Yes. Because the Duggars aren’t going away, not comedically. As long as the Duggars continue being very pious and very religious, I will be making fun of them. And they’re multiplying. As a comedian, you have to look for funny in everything. There is a certain delicious irony that when you read interviews with the Duggars, they’re quite homophobic and bigoted, and yet the show is predicated on how incredibly religious they are and how much they love the Lord.

There was a party at “Glee’s” Chris Colfer’s house last weekend, where he screamed “Mommy dearest!” sitting next to Academy Award nominee June Squibb, doing color commentary with Jane Lynch. You can’t write this stuff. This is the stuff I’m going to bring to the Kennedy Center, because the Kennedy Center audience knows who June Squibb is. That, coupled with a Lady Gaga omelet, coupled with the minute-by-minute Caitlyn updates I’ll be giving them, is so much material it’s going to be all I can do to get off the stage by 10:00.

You are friends with so many celebrities now. Does that make it harder to make fun of them?

A lot of them are finally coming around, and I very much enjoy that. I don’t mind if the occasional Demi Lovato or Lana Del Rey is mad at me. But I appreciate it when a celebrity comes up to me and goes, “Oh, I get it.” Miley Cyrus finally gets it. She goes, “Oh, you’re just kidding.” Yes, Miley. This whole time I’ve just been kidding. I don’t dislike you. I think you’re great. The thing people don’t believe is I’m a genuine fan of 95 percent of the people I make fun of. I was raised in a fast-talking family where you gave as good as you took. And it’s kind of with an affectionate wink that I make fun of these celebrities.

I have many, many things to say about Kirstie Alley. And the last time I saw her, she was very pleasant. And I felt like, “Oh, it’s like a turning point.” I used to think she really, truly loathed me, and now she kind of gets it. She’ll say something to me like, “Oh, God, I’m afraid to say anything to you, because I’m afraid you’re going to put it in your act.” And I say, “Yes, you should know that I am going to put it in my act.” So as long as we have that understanding, we’re fine.

Your New Year’s Eve gig with Anderson Cooper on CNN: Did you think when you’d started it that it would become the annual event that it’s become? You’re like the Guy Lombardo now of New Year’s Eve.

Well, I hope that makes him the Lennon Sisters. Never in my wildest dreams could I imagine how much fun that was going to be. I always say it’s one of my favorite jobs of the year because as much as I love to make everyone laugh, there’s something special about making Anderson absolutely lose it year after year. I have not achieved my bucket list of actually getting him fired yet, but a girl can dream. And we will be doing it again this New Year’s Eve. So I look forward to that. I don’t know if he does, but I don’t care. I was born to it, and that’s enough for both of us.

Catlin is a freelance writer.

Kathy Griffin Saturday at 8 p.m. at the Kennedy Center, 2700 F St. NW. Tickets: $49-$99. 202-467-4600. www.kennedy-center.org.