Bout was arrested in March last year at a luxury hotel in Bangkok, after an elaborate sting operation in which US agents posed as arms buyers.
The US now wants to try him on charges of trying to sell large quantities of high-tech weapons, including surface-to-air missiles to the FARC rebels.
He has been indicted on four terrorism-related charges in New York and could face a maximum penalty of life in jail.
Prosecutors say Bout's long-running career in arms smuggling saw him supply weapons to conflicts in South America, the Middle East and Africa, including to former Liberian dictator Charles Taylor.
Bout has repeatedly denied the charges, claiming he ran a legitimate air cargo business and was in Bangkok at the time of his arrest to discuss selling airplanes to Thai businessmen.