The Italian joined the Spanish backmarker outfit from Force India at the start of the 2011 season and says he signed a long-term contract.
However, the deal was completed when HRT were owned by Jose Ramon Carabante, who sold his stake to investment group Thesan Capital in July.
"I have a contract to race next season with HRT, but the agreement was concluded with the previous owner and now the future is uncertain," Liuzzi told TotalRace.com.
HRT recently parted ways with team principal Colin Kolles following a dispute over their decision to relocate from Germany to Spain.
The team have announced that veteran Pedro de la Rosa will race for them in 2012, but new boss Luis Perez-Sala says they are in no rush to name a team-mate, despite having held discussions with several drivers.
Liuzzi is reportedly battling it out with Jaime Alguersuari, who was recently released by Toro Rosso, and Spanish youngster Dani Clos for the second seat.