"Doria would not get a look in," Diana's former butler, Paul Burrell told ITV's Piers Morgan and Susanna Reid.
He added that Doria would only be pushed to the side, because Diana would love being a grandmother.
"She'd be in her element wouldn’t she? She'd have been thrilled to bits."
Baby Sussex is Diana's fourth grandchild, after William's Prince George, Princess Charlotte and Prince Louis, while Harry and Meghan's little man is Doria's first.
Paul's comments come after Harry opened up about his son's arrival on May 6, telling the world, "How any woman does what they do is beyond comprehension but we're both absolutely thrilled and so grateful to all the love and support from everybody out there.
"It's been amazing so we just wanted to share this with everybody."
WATCH: THE MOMENT BABY SUSSEX IS ANNOUNCED TO THE WORLD
