The Lisa Marie, named after his daughter, was bought by Elvis Presley in 1975 and refurbished to include a master suite with full-size bed and conference room.
Neither plane is airworthy but has been on display at Graceland for more than 30 years for fans to tour.
They are being auctioned off by Julien’s by sealed bids.
Elvis Presley bought the Convair 880 jet in 1975, two years before his death, and spent about $300,000, refitting it and renaming the Lisa Marie. It also features a bathroom with gold taps and a stereo system with 50 speakers.
The tail is adorned with Elvis Presley’s trademark TCB for Taking Care of Business.
The last flight it took was to transport his former wife Priscilla Presley and actor George Hamilton to his funeral.
It was sold by his father, Vernon, in 1978, and had two owners before being bought by a consortium in a joint venture with the owners of Graceland to allow it to be displayed at the tourist hotspot.
The agreement with the owners and Graceland expires in 2015.
The Hound Dog II, a Lockheed JetStar, was bought in 1975 as a stopgap while the Lisa Marie was being prepared. It arrived at Graceland in 1984.
The planes are being sold as one lot, with the option to buy land next to Graceland to display them, independent of the Presley Museum.
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