Vodafone will file an application this month with India's foreign investment promotion board to seek clearance for the investment, the Financial Times reported, citing two people familiar with the situation.
Vodafone could not immediately be reached for comment.
The FT said the size of the investment suggested that the world's second-largest telecoms operator will not up its stake to 100 percent.
In July, India approved raising the foreign investment limit in the telecom sector to 100 percent from 74 percent in a bid to lure capital inflows, prop up a sliding currency and boost growth.
The Financial Times said Vodafone is considering buying out some minority investors including billionaire industrialist Ajay Piramal, who holds 11 percent stake in Vodafone India.
Vodafone owns about 64 percent of Vodafone India, while 25 percent is controlled by undisclosed minority shareholders, who are understood to include Analjit Singh, chairman of Vodafone India, the FT said.