James and Julia, who married in 2012, are already parents to a 6-year-old son, Max, and a 2-year-old daughter, Carey.
Meanwhile, ET caught up with Corden in May, where he opened up about giving advice to Katy Perry while filming Carpool Karaoke.
"I talked to her about [American Idol], and on the day that we shot Carpool, she had to make up her mind that day," the Late Late Show host revealed. "She said, 'What do you think I should do?' and we talked it all out in the car."
"She also talked about a lot of things that she's never really talked about publicly before, so, yeah, it will be fun!" he added.