Bangladesh, a country of more than 160 million people, has already received vaccines from SII as part of an earlier deal for 30 million doses. India's government has also gifted the neighbour 2 million doses of the shot that SII, the world's biggest vaccine maker, is producing for many countries.
"Talks ongoing. Let's see," Health Secretary Abdul Mannan told Reuters.
SII did not respond to a request for comment.
Bangladesh is also due to get a total of 68 million doses of vaccines from a WHO-backed alliance, with the first shipment of around 10 million doses expected by June, Mannan said.
"We have not ordered for any additional doses. As of now our total order is for 30 million doses," Beximco Pharmaceuticals' Chief Operating Officer Rabbur Reza told Reuters.
"Additional orders will depend on the government."