The E! News presenter and her Apprentice winner spouse are expecting their first child via a gestational carrier.
Bill told Us Weekly: "We're kind of in rush mode! We found a great house [in Los Angeles]. It's in the final stages of construction so I'm there every day getting that finished. So we hope to be moving into the house in the next three weeks.
"We have everything [for the nursery] but it's just kind of sitting there waiting to be put in. The nursery's ready to go! So we just have to get the house finished."
He added: "We're gearing up! We had a lesson on swaddling last night and we had another one on changing diapers. So we're enrolling in classes and stuff. We're getting prepped! We're getting it all in before the little guy comes."
However, the couple won't be spending much time in their new house at the start of their son's life as he will be born in Colorado.
Bill added: "The baby won't be born in LA; he'll be born in Colorado. So we're going to go from Colorado to Chicago and then spend September and October in Chicago. And then we'll come back to the West Coast."