Presley died in 1977 of a heart attack after years of drug abuse. He was 42 when he was laid to rest beside his mother Gladys in the mausoleum of the Forest Hill Cemetery in Memphis for two months before Tennessee state officials granted permission for the bodies of both Presleys to be re-buried at the singer's Graceland home.
The New York Times said the auction is to take place June 23 with a starting price of $100,000.
Darren Julien, president and chief executive of Julien's Auctions, told the newspaper he did not categorize the sale of the crypt as "morbid."
"I just consider that if you're an ultimate fan of Elvis Presley, it's an opportunity," Julien said. "It's definitely a conversation piece. Only one person can say, 'Hey, I'm going to be buried where Elvis Presley was.'"