Chetia, the founder general secretary of the United Liberation Front of Asom (ULFA), had sought political asylum in Bangladesh thrice in 2005, 2008 and 2011 after being arrested in Dhaka in 1997.
He is in jail on charges of illegally entering Bangladesh using a forged passport and for possessing illegal foreign currency and illegal arms. His jail term ended in 2003.
"Anup Chetia's jail term is over. Bangladesh is ready to hand him over to India. He has appealed to the Supreme Court of Bangladesh, requesting not to be handed over to India. We (Bangladesh) have no specific law to entertain his appeal," Alamgir told reporters.
He said that after the completion of court formalities and getting the final decision of the Supreme Court of Bangladesh, Chetia would be handed over to India.
Alamgir came to Tripura for the inauguration of an international standard Integrated Check Post at the Akhaurah border near the capital Agartala.
"After a joint effort by both the countries, the extradition treaty was signed recently to make the two nations crimeless. We want to flush out all types of social crimes in both countries," he said.
The minister said there was no Indian militant camp on the Bangladesh soil.
"Bangladesh Prime Minister Sheikh Hasina has already said that the country's soil would never be used by insurgents of India," Alamgir said.
"We have requested the Indian authorities to give us the particulars of Indian militants hiding in Bangladesh, if any, and then we would take appropriate action. If there is any militants in Bangladesh, we would certainly hand them over to India."
The Bangladesh minister also said there was no political crisis in his country. "We are determined to hold elections as per the constitution."
Meanwhile, Indian home minister Sushilkumar Shinde said in reply to a question that the process was on to exchange enclaves between the two countries.