The plane was flown in from Siem Reap in neighbouring Cambodia in late 2007 and has been unclaimed ever since.
An airport official told the BBC that they believe the owners could be an airline based in Cambodia.
The official said that if it remains unclaimed, the plane will have to be sent for scrap.
The plane has a Cambodian flag on its fuselage and is emblazoned with the name Air Dream, but the authorities say they have no information about the airline.
Earlier, one security official at Noi Bai airport told the BBC's Vietnamese Service that the plane belongs to bankrupt budget Cambodian airline Royal Khmer, but this is not certain.
Permission was originally given for the plane to remain at the airport while essential maintenance was carried out but these repairs have not been done.
Online newspaper VietnamNet reported that the owners could be unable or unwilling to pay the required airport parking fees.