He said: "Meghan will take her kids on a subway. They'll have chores, and jobs one day. They won't be spoiled."
It comes after it was reported that Harry and Meghan would not be seeking a royal title for their first child, to enable them to lead a normal life.
If the new royal baby is a boy, he will likely become the Earl of Dumbarton, a subsidiary title given to Prince Harry on the day of his wedding, while a girl would become Lady Mountbatten-Windsor.
As Harry is not in direct succession to the throne, the couple's baby will be unlikely to be a full-time royal.
The Duke and Duchess are thought to be considering following in the footsteps of Princess Anne who famously turned down the offer to give her children royal roles in a break from tradition.
Both Zara Tindall, formerly Zara Phillips, and Peter Phillips do not carry a royal title, unlike their cousins Princess Eugenie and Princess Beatrice.
The latest reports come after it was suggested Meghan's mother Doria, 62, is set to get her own place in the UK in order to be closer to her grandchild.
The yoga instructor, who is currently based in LA, is understood to be considering spending part of the year in England.
Before Meghan's pregnancy was announced, Doria was said to have been taking baby-care classes near her home.