The two parties initiated talks earlier this week for a stake in Future Retail, they said.
"They have initiated talks and these are still in early stages," a person privy to the development said.
The move came after Future group firms defaulted on loans taken against the pledged shares of Future Retail in March, which also impacted its share price.
Recently, rating agencies such as Standard & Poor's and Fitch downgraded the credit ratings of Future Retail after the default.
When contacted, the Future Group denied any such discussion saying that they are "speculative in nature".
Amazon India said the company does not have any comment to offer on this matter.
At the end of December quarter 2019, the promoter Group entities, which include Future Corporate Resources and Future Coupons, held 47.02 per cent share in Future Retail.
Future Retail operates over 1,500 stores that cover over 16 million square feet of retail space in 400 cities. It has large format stores, Big Bazaar, its flagship chain, besides small store neighbourhood retail chains, EasyDay Club and Heritage Fresh.
In August last year Future Retail had informed stock exchanges that Amazon.Com NV Investment Holdings LLC would acquire 49 per cent stake in Future Coupons Ltd from their promoters, led by Kishore Biyani, for an undisclosed amount.
At that time Future Coupons held 7.3 per cent stake in Future Retail.
As part of the agreement, Amazon was also granted a call option, which allowed the US ecommerce major an option to acquire all or part of the promoter's shareholding between the third and tenth year.
Amazon also has a stake in other retail chains in the country — Shoppers Stop and More. In 2017, retail major Shoppers Stop had announced raising Rs 179.26 crore from Amazon.com Investment Holdings LLC through an issue of equity shares, which translated to just over 5 per cent shareholding for the American company.
In September 2018, Amazon said it has co-invested in Witzig Advisory Services, the entity which had acquired Aditya Birla Retail''s ''More'' chain of stores in India.