The 38-year-old Duke of Cambridge, the third in line to the U.K. throne, kept his diagnosis secret, unlike his father, Prince Charles, who had announced his own positive COVID-19 test in March, the reports said.
When reached by NBC News on Sunday night, Kensington Palace would not confirm or deny the reports about William.
In recent months, he and wife Kate Middleton have been social distancing at their family home Anmer Hall in Norfolk, England.
In late March, weeks after the start of the coronavirus pandemic, Charles revealed that he had tested positive for COVID-19 and had mild symptoms. The 71-year-old has since recovered.
U.K. Prime Minister Boris Johnson, 56, was diagnosed with the coronavirus around the same time and spent a week in the hospital, including time in the ICU.