"Miss, Lamia 933 has a total failure, total electrical failure, without fuel," a voice identified as that of the plane's pilot is heard saying on the recording.
The control tower immediately told the pilot that he had an open runway, Efe news agency reported.
A total of 71 people were killed when the plane chartered by soccer club from Bolivia's Lamia airlines crashed near the airport in the northwestern city of Medellin.
Authorities initially said the British-made RJ85 regional jet was carrying 81 people, but they later learned that four passengers listed on the manifest never boarded the plane.
The plane was carrying Chapecoense players, executives, coaches and other staff, along with special guests, journalists and a crew of nine.
The aircraft went down around 10 p.m. on Monday nearly 17 kms from the airport.
The survivors, according to the country's aviation agency include three players of the soccer team, two members of the flight crew and a journalist.
The team's goalkeeperinitially survived the crash but died on his way to the hospital, officials said.
Both of the doomed flight's black box recorders have been recovered and are already being examined by experts, BBC reported.
British investigators are to help authorities in Latin America as the plane was manufactured in the UK.