The supermodel has had plans for a nursery drawn up as part of a 1million- pound renovation to the family home.
Now Moss, who already has 7-year-old daughter Lila by her ex, Jefferson Hack, is getting ready for a new arrival after she weds The Kills' guitarist in July.
"Jamie and Kate are on Cloud Nine at the moment," the Sun quoted a source close to the pair as saying.
"Now they have made the commitment to each other, the next step is a family. Jamie has been brilliant with Kate's daughter Lila, which has made her broody for another child.
"He's genuinely devoted to Lila and that's one of the main reasons she's getting married.
"Jamie does Lila's homework with her, he's teaching her to read music and play guitar. He is also teaching her to paint.
"The first person Kate told of the engagement was Lila, who ran around the house punching the air. They would love a child of their own," the source added. (ANI)