"It's annoying but in a really great way, [with] emails every day," Josh Brolin said of stepmom Barbra Streisand checking up on his baby girl on the way

Josh Brolin and wife Kathryn Boyd are expecting their first child together (a baby girl!) — and no one is more excited than his stepmother Barbra Streisand.

“My wife got her a bracelet that said ‘Grandma’ on it and she started crying,” the Sicario: Day of the Soldado actor, 50, recently told PEOPLE and Entertainment Weekly’s Editorial Director Jess Cagle for SiriusXM’s EW Radio Spotlight.

“She is one of those … it’s annoying but in a really great way, [with] emails every day and like, ‘Hey, I thought of this name, what do you think of that? … When can I come over and feel the baby?’ ” said Brolin, who is already a father to 28-year-old daughter Eden and 30-year-old son Trevor.

“You realize she follows all the apps, so you know the baby is as big as a banana, which is always weird to me. I don’t want to think of my baby as a banana or any kind of fruit or vegetable,” the soon-to-be father of three joked.

“She is really into it and I love that she is into it. I mean, it’s like very typical Jewish grandmother who is saturated by this event. It’s awesome,” Brolin added of Streisand, 76, who has been married to his father James since 1998.

Want all the latest pregnancy and birth announcements, plus celebrity mom blogs? Click here to get those and more in the PEOPLE Babies newsletter.

Premiere Jonah Hex LA, Los Angeles, USA
Credit: Matt Sayles/AP/REX/Shutterstock

James Brolin, Barbra Streisand and Josh Brolin

In late May, Brolin and Kathryn, who tied the knot in September 2016, announced they were expecting with a sweet Instagram post. “There’s a new sheriff in town and she’s no bigger than a sweet potato. Hang on to your hats,” he captioned a photo series of the mom-to-be showing off her bare baby belly while out on a hike.

Also on Wednesday, Brolin spoke with Good Morning America co-anchor Michael Strahan about his eight-time Grammy-winning stepmom.

“[Barbra] is, like, in our face. She’s calling all the time, emailing all the time, she has name suggestions, we got her a bracelet that says ‘Grandma’ on it [and] she started crying. She’s into it, man. Really, really into it,” he said.

"Jonah Hex" Los Angeles Premiere - Red Carpet

Barbra Streisand and Josh Brolin

Brolin opened up about fatherhood on social media in April, sharing a photo of his two adult children in honor of Easter.

“There is no duo I love more than this punk rock duo, my two kids. They see the world through the ever revolving kaleidoscope it’s meant to be experienced through,” the actor wrote.

“I have been blessed with a potpourri of emotional fireworks because of them. And, over a quarter century into it, I am a better man because of them. I might not be as mature as they are, but there’s still time,” Brolin added.