The existence of the tapes was revealed by US magazine The Globe, which quoted a source, who is said to be one of Diana's "closest friends".
The tape suggested Diana had a chilling premonition about her death because of worries that she had made some dangerous enemies. Her decision to make the recording add weight to the arguments of those who believe her car-crash death in the year 1997 was no accident, but the outcome of a dark conspiracy, the US magazine says.
Diana's messages urged her oldest son and his future wife to: "Cherish your children for me... let them know I'll love them and watch over them..."
Although Diana never met Kate Middleton, now Duchess of Cambridge and wife of Prince William, the US magazine claimed the tapes show Diana imagined William's bride to be "beautiful, smart and independent".
The voice of the tape stated: "I know I'd adore you and we'd be fast friends. You'd have to be someone truly special. If you weren't, you wouldn't be my William's wife."