But his Grey's Anatomy costar Jessica Capshaw tells Usmagazine.com the actor, 36, isn't keeping quiet about being a dad on the set of the ABC drama.
"We were working the other day, and he's going through all the new prospective dad things," Capshaw, 33, told Us Wednesday at a Judith Leiber store opening in Beverly Hills. "He's like, 'I don't know what I'm getting into; what's going to happen; what kind of dad am I going to be?'"
She doesn't think he'll have any problem.
"He'll be a great dad," she told Us. "He's such a nice guy, and he's really funny. He's very warm and sweet."
"I say sleep now," said actress, who has a son Luke, 2, with husband Christopher Gavigan. "Because I couldn't sleep for two years! Now I can sleep. Even when they're sleeping, you're going, 'Are they okay?'"
Meanwhile, two of her costars — Ellen Pompeo and Katherine Heigl — recently became moms for the first time.
Pompeo welcomed daughter Stella on Sept. 15. The same week, Heigl brought home her adopted 10-month-old daughter, Naleigh.
"I have tons of well wishes," Capshaw told Us. "When we get back, we'll have to have a baby party!"