A pilot can be heard repeatedly requesting permission to land due to an electric failure and lack of fuel.
Just six of the 77 people on board the plane survived.
The team, Chapecoense, had been due to play a cup final on November 30. Fans instead have been gathering at their stadium for a memorial event.
The leaked conversations between the flight crew and a Colombian air traffic controller give a glimpse of the frantic, final moments of the doomed plane.
The pilot and can be heard warning of a “total electric failure” and “lack of fuel”.
Just before the tape ends, the pilot says he is flying at an altitude of 9,000ft (2,743m). The plane slammed into a mountainside near the Colombian city of Medellin on November 28.
That there was no explosion when the plane came down also points to lack of fuel, with one Colombian military source telling the AFP agency its absence was “suspicious”.
It is not known why the plane was out of fuel: whether it was due to a leak or because there was not enough on board.
Investigators have yet to announce any single cause for the crash and a full analysis is expected to take months.
Chapecoense team was flying to Medellin for what would have been the biggest match in their history – the final of regional tournament the Copa Sudamericana.
The team lost 19 players in the crash. Twenty journalists were also killed.
Among the survivors, Chapecoense said that two players remained in a critical but stable condition, while the club’s goalkeeper had had one leg amputated and might still lose his other foot.
An injured journalist also remained in critical condition, the club said.
Another survivor, flight technician Erwin Tumiri, said he was still alive because he followed safety instructions.
“Many stood up and started shouting,” he said.
“I put the suitcases between my legs and assumed the brace position.”
Brazil declared three days of official mourning and thousands of fans in the city of Chapeco held a vigil in their home stadium to mark their loss.
Chapecoense directors say they expect up to 100,000 to attend collective funerals once all the bodies have been identified, most likely on December 2 or December 3.
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