In June 1953, an 18-year-old Presley went to the Memphis Recording Service to record 'My Happiness' and 'That's When Your Heartaches Begin'. He wanted to find out what his voice sounded like on record and paid USD 4 for the session.
He returned to record sessions for Sun Records the following year and went on to become the King of Rock and Roll. The auction will take place in January, reported BBC online.
It will be one of 68 rare artefacts to be auctioned at his former home of Graceland in Memphis.
Presley was said to have made the recording partly as a present for his mother.
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But the family did not have a record player, so he took it to a friend's house to listen to the results of the session and left it there.
This will be the first time it has come up for public sale.
The other items in the auction will include his driving licence, issued in 1952, a 1955 contract to perform on the Louisiana Hayride radio and TV programmes and a jacket worn in the film Viva Las Vegas.