Ali Leonardi of Adam Air's legal department said families have to submit the birth certificate of their missing relatives.
"This will need time to process. But if all requirements are completed, we want to settle this immediately."
Weeks of intensive search has only yielded small pieces of the wreckage found floating in the sea or washed up on beaches off Sulawesi's western coast, but no bodies.
Sophisticated equipment has failed to
locate the missing jet [EPA]
Rescue officials have said that Adam Air's Boeing 737-400 could have crashed into the sea before disintegrating into small pieces.
So far, efforts to detect the locator beacon from the missing aeroplane has failed despite the help of sophisticated equipment and experts from the US and Singapore.
The jet was flying from Surabaya in East Java to Manado in northern Sulawesi when it disappeared from radar screens on New Year's Day shortly after the pilot registered concerns about crosswinds. No distress signal was issued.
Eddy Suyanto, who is heading the search, has said that a body was unlikely to have survived the disaster in one piece, considering that parts of the plane found so far were mostly small.