"My dad keeps joking that we need to name him George," former first daughter Jenna Bush Hager tells PEOPLE for this week's issue of dad George W. Bush

Jenna Bush Hager is giving her father a grandson!

After previously welcoming two daughters, the new co-host for Today‘s fourth hour announced last week that she’s expecting her third child, and first baby boy.

Opening up about how her parents, former president George W. Bush and wife Laura Bush, are taking the exciting news, Hager tells PEOPLE they couldn’t be happier — especially her dad.

“They’re over the moon about it,” she shares in this week’s issue, on newsstands now. “Everybody is so excited.”

The soon-to-be mother of three — already mom to daughters Poppy Louise, 3½, and Margaret “Mila” Laura, 6 — adds that her father wouldn’t be upset if he and his grandson end up sharing the same name.

“My dad keeps joking that we need to name him George,” continues Hager, 37, before pointing out that she and her husband, Henry Hager, haven’t made up their minds yet about what they’ll be calling their baby on the way.

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Jenna Bush Hager and family
| Credit: Jenna Bush Hager/Instagram

Whether or not the former president ends up sharing his moniker with his grandson, Hager says he’s just looking forward to finally having a little boy in the family.

“We had two girls. That’s all he’s ever known,” she tells PEOPLE. (In addition to having two granddaughters, her father is also a proud parent to two daughters of his own: Hager and her twin sister, Barbara Pierce Bush.)

Although Hager shares that her dad absolutely adores “our girls,” the former first daughter adds that it’ll “be nice for him to have a little fishing buddy as well.”

Of course, choosing a name for their son is just one of many tasks on the couple’s to-do list. “I know I’m far along in my pregnancy, but because we were keeping it quiet and working on the show, there’s so much I have to do,” Hager tells PEOPLE, revealing that she’s “due in the late summer.”

hoda kotb and Jenna bush hager
Hoda Kotb and Jenna Bush Hager
| Credit: Nathan Congleton/NBC

RELATED VIDEO: Hoda Kotb Opens Up About Adjusting to Life as a Mom of Two: “In a Blink, Life Changes”

Opening up about her “unexpected pregnancy,” Hager shares that having a child while taking over as new co-host for Today‘s 10 o’clock hour wasn’t a part of her and her husband’s plan.

“We really hadn’t planned to even have a third baby and it feels like this blessing that I hadn’t even asked for,” she explains. “Is the timing ideal? Not really. We are launching something new and I’ll be taking maternity leave this fall. But it’s not about that.”

But she also says her co-workers have been nothing but supportive to her and her new co-host Hoda Kotb, who recently welcomed daughter Hope Catherine via adoption on April 12.

“There was no hesitation when I told anybody at work. It is a beautiful journey for you and your family. And I know they feel the same way for Hoda,” Hager tells PEOPLE.

hoda kotb
Hoda Kotb covers PEOPLE with daughters Hope and Haley
| Credit: Brian Doben

Hager announced her own pregnancy on April 22, six days after Kotb revealed she had adopted her new bundle of joy, daughter Hope.

“These decisions about expanding our families are personal … our work is wonderful and I’m thrilled with how our show is going. But it’s really forward thinking,” Hager tells PEOPLE.

“And the fact that Hoda and I get to start this journey together [with babies] who will be months apart and we get to do the show together,” she continues, “we are creating these new things together. New lives, and a new show as a team.”

For more from Jenna Bush Hager and other Today show moms, pick up the latest issue of PEOPLE, on newsstands now.