Jenna Bush Hager Opens Up About Her Kids, Reading and New Kitten 'Hollywood Hager'

Jenna Bush Hager's kids are following in her footsteps.

Speaking to PEOPLE at a party Thursday to celebrate four years of her Today book club, Read With Jenna the 41-year-old revealed that her three children — daughters Mila, 9, Poppy, 7, and son Hal, 3 — also have the reading bug.

"They love to read," the Today with Hoda & Jenna host said of her kids, whom she shares with husband Henry Hager. "I feel like when you're modeling things like that, that's what they do. So, my kids are loving to read. They are constantly hanging together, playing."

As for what else her children are into, Bush Hager said her brood is "obsessed" with their new furry family member, kitten Hollywood Hager.

"It's a huge decision, but it's the best decision," she said of adopting the feline, who they brought home over the holidays. "Mila is responsible for everything. Litter box, feeding, all the above."

Bush Hager introduced her new furry companion to her 1.3 million Instagram followers at the end of January.

"Do you see why we call her Hollywood?" Bush Hager asked in the video. "She's beautiful. But we call her 'Holly' for short. Holly, middle name 'Wood,' last name 'Hager.' "

She captioned the post, "Instagram, meet Hollywood! My eyes are red from cat allergies, but I love her."

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The star also discussed with PEOPLE how she finds time to read as a busy mom at the Read With Jenna event, which was attended by her Today colleagues Savannah Guthrie and Sheinelle Jones.

"I read whenever I can," she said. "So I read in the morning, I read when I'm getting my hair and makeup done, I read in the evening." Adding that picking up a book is her "greatest joy," she continued, "I don't watch so much television. I love doing it."

Bush Hager also revealed how Read With Jenna came about and how it has developed into something that is beyond her "wildest dreams."

"Well actually one of my bosses here was like, 'I don't know that people read that much,'" she explained. "And I was like, 'Yes. People read, my friends read.' And it was kind of a dare, I mean, for lack of a better word."

"It's become this incredible community of writers and authors and of Today show viewers who are reading books that are different maybe than their everyday life," she continued. "It's bringing everybody together and I'm just like, it's beyond my wildest dreams."