But royal sources said the story wasn't true. And St James' Palace staff just said they didn't comment on Prince Williams' private life.
The story is still likely to spark more rows about the royals and hunting.
In the past, animal rights campaigners have criticised members of the royal family who take part in blood sports.
William has joined his dad, Prince Charles, on an English fox hunt.
'Crude way to kill'
Animal rights people have already reacted angrily to the story.
"Spearing an animal is a crude way of killing it, and not guaranteed to kill the animal quickly," said a spokesman for the World Society for the Protection of Animals.
"We have hundreds of thousands of members and when they go on holiday they like to watch animals in the wild, not try to take them out of circulation."
Prince William is in Kenya for a month-long summer holiday with seven friends.
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Fox hunting is cruel and should be banned
