Presley, 44, discussed her iconic rock 'n' roll father, who died 35 years ago this week, alongside her mother Priscilla during a half-hour talk before Elvis fans at the family's Graceland mansion in Memphis, Tennessee.
It was the first time the singer-songwriter, whose latest album Storm and Grace came out in May, had participated in an open panel discussion at the annual Elvis Week festivities.
"Really, I just want them to be really good at whatever they want to do," she said when asked about her children Riley Keough, 23, Benjamin Keough, 19, and three-year-old twins Harper and Finley Lockwood.
Riley, who appears in director Steven Soderbergh's male stripper film Magic Mike, is doing "incredibly well" in her acting career, while music-loving Benjamin is "swinging back and forth" between bass and guitar, said Presley.
Of "the little ones," she said Finley "is definitely going to sing... that child loves music," while potential thespian Harper can recreate any movie she sees "scene by scene, line by line, exactly as she saw it."
Asked what the twins make of their iconic grandpop, Presley said: "They are very, very, very proud. 'That's my grandfather! I want to see my grandfather!' They have such a sense of pride. It's really cute."
Presley had her older children with her first husband, musician Danny Keough, and the youngest ones with her current spouse, music producer Michael Lockwood. She was also married to the late Michael Jackson and actor Nicolas Cage.