The report cited unidentified palace sources and The Sun newspaper, who said William kept his phone and video engagements without revealing his diagnosis because he didn’t want to worry anyone.
Kensington Palace declined to comment on Sunday but did not deny the report.
The newspaper said William had been treated by palace doctors and followed government guidelines in isolating at the family home of Anmer Hall.
Prince Charles had mild symptoms of COVID-19 in March. During his first public engagement after his recovery, Charles revealed that he lost his sense of taste and smell while ill.
William made a public appearance in mid-October with his grandmother Queen Elizabeth II, who was making her first public engagement outside a royal residence since early March. They met scientists from the Defense Science and Technology Laboratory in Porton Down, in the south of England.