A "friend" of the royal couple told the British paper that Kate announced the date at a family barbecue, The Daily Mail reported Sunday.
"Some of Kate and William’s closest pals were at a barbecue hosted by a family friend of the Royals recently," the source said.
"They were all discussing the fact that Kate’s baby is due to be born on July 13. Everyone was very excited," the source added.
A July 13 due date puts the royal baby's birth smack dab into the middle of Queen Elizabeth's Coronation Festival, which celebrates 60 years since she was crowned. The festival takes place from July 11 to July 14.
"‘We have only said that the Duchess is due in July. Anything further would be speculation," a palace rep said of the report.
While royal representatives have yet confirmed the baby's sex, one report has suggested that William and Kate might be expecting a boy.
A source told People last week that Prince Harry has been telling everyone he's excited about the prospect of a nephew.