But India has not met requests for granting the manufacturers indemnity from lawsuits.
India's junior health minister told parliament on Tuesday that a team of officials had been formed to engage with the vaccine makers.
"This team is in continuous dialogue with Pfizer, Moderna and Johnson & Johnson to discuss and address various issues including the issue of indemnity," Bharati Pravin Pawar said.
Pfizer said it was in discussions with authorities to make its vaccine, developed with Germany's BioNTech, available in India. It declined to share details of the negotiations, citing confidentiality.
Moderna and J&J did not respond to requests for comment.
India's health and foreign ministries did not respond to requests for comment on the indemnity issue.
Vaccine alliance Gavi, which co-leads the COVAX facility, said legal protections for vaccine suppliers were mandatory.
"All facility participants must have signed indemnity agreements with the manufacturers in question in order to receive doses through COVAX – which would also be true for doses received via bilateral deals," a Gavi spokesperson said in an email.
India is heavily reliant on the AstraZeneca vaccine produced by the Serum Institute of India (SII). Bharat Biotech - maker of India's only approved home-grown shot - is struggling to boost supply.
SII has already told the government that any indemnity for foreign vaccine companies should also apply to Indian producers.
One government source said Moderna's Indian partner Cipla had offered to bear some legal responsibilities for the vaccine's use in the country, but that the proposal had been rejected by the US company.
"The government cannot give indemnity to anyone," the official said, declining be named as the discussions were private and no decisions had been finalised.
"The government is saying domestic companies can give indemnity on behalf of their foreign partners."
Cipla declined to comment ahead of its financial results.
India has administered 441 million total vaccine doses, the largest of any country after China. But only 10 per cent of its adult population of about 944 million people has been inoculated with both doses, with 47 per cent receiving at least one shot.