Prescription drugs were found in Prince's possession when he died, according to US reports.
Officials told NBC News the painkillers were discovered in his Minneapolis home - but it is as yet unclear if they played any part in his death.
The pop star died aged 57 on April 21 after being found collapsed in a lift at his Paisley Park estate.
Prince's body has been cremated in a private family ceremony, according to reports.
Family and friends were seen arriving at Paisley Park on Saturday, where it is believed a private memorial was held.
The Associated Press, citing publicist, said that Prince's body had been cremated and a celebration of his life had been held.
The pop icon, a Jehovah's Witness who died aged 57, is said to have been secretly cremated after his body was released to his family on Friday afternoon, following a post-mortem examination.
The painkillers were reportedly found in the singer's possession when he died - but it is unclear if they played any part in his death.
Mourners celebrate pop icon at private memorial at Paisley Park estate.
Star's ex-manager voiced concerns over whether whoever inherits the star's fortune, and valuable catalogue of works, will know what to do.