CNN Travel reports that Elvis Presley's private jet is on the auction block. The decrepit plane does not have an engine, the cockpit's a mess and the velvet seats have lost their plush. But when there's a chance to own Elvis Presley's customized private jet, fans might be willing to overlook the rust that comes with sitting on a runway in New Mexico for 36 years. The 1962 Lockheed JetStar 1329 was owned by the king of rock 'n' roll star and his father, Vernon.