Niels Holck, 62, has admitted to parachuting four tonnes of weapons into the state of West Bengal to help locals fight government authorities.
He was the only one of seven smugglers who managed to escape after the Indian Air Force intercepted their returning plane.
The others, five Russians and a Briton, were sentenced in Kolkata to life imprisonment in 2000, but all were eventually released.
India regards the Dane, also known as Kim Davy, as the mastermind of the operation, which saw the delivery of hundreds of assault rifles, pistols, anti-tank grenades, rocket launchers and thousands of rounds of ammunition.
New Delhi has relentlessly pursued attempts to have him stand trial in India, and the affair has been a stumbling block in Danish-Indian relations.
Holck was arrested in Denmark in April 2010 after Danish authorities reached a deal with India over the terms of his extradition, including a promise that he would not be given the death penalty and would serve any sentence in Denmark.
But a Danish district court in 2011 overturned the authorities' decision, saying he risked mistreatment in India.
An appeals court later upheld the district court's ruling.
Holck's lawyer, Jonas Christoffersen, told AFP this week that his client would appeal if the Hillerod district court on Thursday orders him extradited.
"He's frustrated that the case has dragged on for so long," Christoffersen said.
"Now he's hopeful that it will come to a close and that once it has gone through the Danish legal system, it will be clear that he will never be extradited to India."
"He is going on with his life, but he cannot travel. He has his life in Denmark but it's a burden on him," he said. "He's been called a terrorist without any factual merit for 28 years."
In his 2008 autobiography titled "They Call Me a Terrorist", Holck recounts the delivery of the arms during a flight that left from Bulgaria.
Prosecutors are expected to appeal if the court does not order his extradition.
The Hillerod district court's decision is expected around 1:00 pm (1100 GMT).
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