Jack and fiancée Lisa Stelly welcomed their first child, a daughter named Pearl, late last month.
Talking to Us Weekly, Kelly expressed her enthusiasm at being a new aunt.
"[Pearl's birth] is the most amazing thing that has ever happened to our family. I could not be happier," the 27-year-old explained.
"[Pearl's birth] made me realise how badly eventually I want to have children, but it also made me realise I'm not ready yet."
Kelly also had nothing but positive things to say about Jack's parenting skills so far, adding: "He's just so happy and he's so good with the baby. It's unbelievable."
Jack and Kelly's mother Sharon Osbourne has described becoming a grandmother as an "amazing event".