Buckingham Palace declined to comment on the report, which cited "medical sources" as saying the diagnosis was made in April.
"Medical matters are personal and private.
We are not putting out a statement. The prince continues with his engagements as normal," said a royal spokeswoman.
According to the newspaper, the 87-year-old was diagnosed with prostate cancer in April when he spent three nights at the private King Edward VII Hospital in London.
At the time Buckingham Palace said he was treated for a chest infection.
But the Standard quoted a cancer specialist as saying "It's become an open secret within the medical community that Philip has prostate cancer.
"If he'd had a serious chest infection that was so worrying it required hospitalization, he wouldn't have walked in and out of there smiling and been 'sitting up in bed replying to letters'," added the unnamed specialist. On Wednesday the prince was in Cowes on the Isle of Wight for the annual sailing week, the royal sp