(aceshowbiz.com) - The rumor mill goes into overdrive again as new claim on the twins that Lisa Marie Presley is carrying has just emerged. According to the New York Daily News newspaper, the singer is having a twin son and daughter. That isn't the one and only detail that is exposed about the twins as their possible names have also been outed. The newspaper claimed further that intending to pay tribute to her late singer father Elvis Presley, Lisa is planning to name her new son Jesse, after Elvis' identical twin brother who was stillborn. A source close to her, moreover, revealed that she's going to name her daughter Gladys Love after her paternal grandmother. Claim on the not-yet-born twins' sex and names comes less than a week after Lisa's mother Priscilla Presley confirmed in an interview with Entertainment Tonight last week that her daughter is pregnant with twins and due to give birth in the fall. Confirming her pregnancy with the twins in a "confirmation under the gun" on her MySpace Celebrity Blog on March 6, Lisa however willingly exposed her baby bump in a series of semi-naked photos taken by celebrity photographer Davis Factor for the September issue of Marie Claire. The twins will be Lisa's first child with current husband Michael Lockwood. They will join brother Benjamin Storm Keough and sister Danielle Riley Keough, both of whom are Lisa's children with her first husband Danny Keough.