According to sources, the deal could be worth about Rs. 2,000 crore. The figure could not be independently verified. The transaction is likely to be announced on Thursday.
Myntra has sent invitations to the media for a conference in Bangalore tomorrow to announce a "strategic development" but did not divulge further details.
(Also see: Flipkart and Myntra to Merge This Week: Report)
The stake acquisition has been in the works for a few months now, with the final details being worked out in the past few weeks.
"We will be unable to comment on market speculation at this stage," a Flipkart spokesperson said.
India's e-commerce market has seen huge growth in the past few years as more people log on to the Internet to shop.
While apparel and electronics are bestsellers for most e-commerce firms, categories such as home decor and household items are also popular.
Flipkart started in 2007 as an online bookstore and now sells products across categories, including fashion and electronics. It now also sells white goods and furniture.
Led by increasing Internet penetration and youngsters shopping online, Flipkart's annualised sales crossed $1 billion (over Rs. 5,900 crore) a year ahead of target.
The company planned to reach the billion dollar mark for gross merchandise value by 2015.
It also operates under the marketplace model, which allows retailers to offer products on its platform.
Since its inception, the Bangalore-based firm founded by Sachin Bansal and Binny Bansal has raised over $500 million (Rs. 3,000 crores approximately) from investors including Naspers, Tiger Global, Accel Partners, Dragoneer, Morgan Stanley, Sofina and Vulcan Capital.
Last year, it raised $360 million (Rs. 2,100 crores) from private equity firms, one of the largest funding deals in the Indian e-commerce space.
Myntra sells products from over 650 brands like Nike, HRX by Hrithik Roshan, Biba and Steve Madden and clocked revenue of about Rs. 1,000 crore in the previous financial year.
It aims to double its revenue in this financial year as it expands its seller base and adds products.
Myntra has about 100 sellers on board and plans to increase this number to 1,000 by fiscal end.