Days after the Duke gave his backing to a campaign against elephant poaching, leading primatologist Jane Goodall said William had told her he would "like to see all the ivory owned by Buckingham Palace destroyed".
The Royal Collection contains some 1200 artefacts containing ivory, dating back hundreds of years.
William's father, the Prince of Wales, has reportedly asked for all ivory items at his Clarence House and Highgrove homes to be removed from sight during the past few years.
Conservative MP Zac Goldsmith applauded the duke's stance on ivory, saying: "It's difficult to imagine a stronger symbol of the horrors of ivory than Buckingham Palace publicly destroying its own. Good for Prince William for pushing this."
A spokesman for the Duke refused to confirm or deny the comments.