He said: "She's [doing] amazing. This is so perfect for her. She's just loving this moment now.
"[She] glows all the time, [she's] as happy as can be!"
And Ken has already decided what to give the little girl – who is expected to be named Maxi – when she makes her way into the world in the next few weeks.
He told US Weekly: "I got her two really cool heirlooms that she can have. One will be in the family forever … and be passed on to generation after generation."
Meanwhile, Jessica has been using her down time to reconnect with her musical side and pen lullabies for her first born.
A source said: "She talks to the baby and already feels like she knows her. She sings to her all the time, too. What's really sweet is that the baby already has songs written especially for her!"