TMZ said Jung, serving time on a drug smuggling conviction, was in talks with producers from National Geographic Channel about a documentary on his life.
TMZ said calls to the production company weren't returned.
Jung, serving time in at the medium security Federal Correctional Institution's La Tuna Prison for men in Anthony, Texas, reportedly was talking to the producers of National Geographic's "Locked Up Abroad" about a show on his life in prison.
TMZ said Jung's business partners were expected to meet with producers as soon as next week.
TMZ is owned by Time-Warner, based in New York.
2014: The Year in Music [PHOTOS]