An airport official raised the concern after checking the plane's flight plan, Bolivia's Deber newspaper said.
Seventy-one people died in the crash, including members of a Brazilian football team. Six people survived.
Bodies of the victims are due to be repatriated to Brazil.
Colombian authorities have said evidence is growing that the British-made BAE 146 Avro RJ85 aircraft ran out of fuel as it tried to land at Medellin airport. Experts say it was flying at, or very near, its maximum range.
In a leaked tape, the pilot, Miguel Quiroga, can be heard warning of a "total electric failure" and "lack of fuel".
On Thursday, Bolivia's aviation authority suspended the operating licence of charter airline LaMia, which was part-owned by Mr Quiroga, and two other aviation officials.
In the report carried in Deber, the Bolivian airport authority official at Santa Cruz airport said she raised concerns that the plane's fuel load was only enough for the exact flight time.
The paper said she described how the airline's clerk, who died in the crash, had told her the pilot was confident he had enough fuel. Despite her concerns, the flight plan was passed on to Bolivian air control.
Bolivian officials have not yet commented on the report.