Prince William and Kate Middleton welcomed their first child into the world in a London hospital on July 22, reported Daily Telegraph.
"They sent William and Kate mini versions of Kanye's clobber, including skinny jeans and hoodies," a source said.
The royal couple are currently enjoying their first weeks of parenthood out of the spotlight, after introducing their son to the world last week.
Kardashian, 32, has meanwhile been in hiding since giving birth to daughter North West on June 15.