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 stayed awake for 154 hours before his death, his brother-in-law has claimed.
Maurice Phillips reportedly claimed the 57-year-old singer had worked for six days without sleep when friends and family held a private service at the compound on Saturday.
Mr Phillips, who is married to Prince's sister Tyka Nelson, is said to have told fans outside Paisley Park: "He worked 154 hours straight. I was with him just last weekend. He was a good brother-in-law."
The mayor of Chanhassen, the city which is home to Paisley Park, where Prince lived, said discussions were taking place to stage a public service in honour of the superstar.
"It's clear his friends and family would support the idea," Denny Laufenburger said.
A private funeral service at a local church is expected to take place in early May, he added.
Prince was found collapsed in a lift by staff members on Thursday morning, more than 12 hours after he was last seen alive when he was dropped off at Paisley Park.
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.