A government minister and official at Prime Minister Narendra Modi's office told the Reuters news agency that cabinet had cleared the bid.
An announcement was expected to be made over the weekend during Japanese Prime Minister Shinzo Abe's visit to India.
China is also bidding to build high-speed bullet train lines in India.
The highly-anticipated multi-billion dollar deal is being touted as one of the biggest foreign investments in India's ageing infrastructure.
"We expect to make an announcement during the visit," the official told Reuters, adding that issues had been sorted out ahead of Prime Minister's Abe visit, which begins on Friday.
The bullet train line is expected to link the financial capital Mumbai and Ahmedabad in the state of Gujurat, cutting the 505km journey from at least eight hours to just two.
Japan is expected to lend India more than half the cost for the project - about $8bn - at very low interest rates for up to 50 years.
The Modi government has committed to invest $137bn in the country's vast, but antiquated railway system over the next five years.
Last month, US's General Electric and France's Alstom also won billion-dollar contracts to provide India's railways with new locomotives.
With air fares still out of reach for many people - train is the way most Indians make long-distance journeys across this vast country.
Tickets are cheap but limited and often need booking months in advance, all for the privilege of riding in carriages that are usually old and fairly rickety.
If the first bullet train really can be up and running in just seven years it'll be the most spectacular outcome of Narendra Modi's pledge to invest $137bn in the antiquated railways.
But for most passengers who want more comfortable, reliable trains which can carry more people, the recent multi-billion dollar contracts awarded to GE and Alstom to build new locomotives for routes across the country will have a greater impact than this one sleek, shiny, high-speed service.
India's government has approved a $14.7bn (Â£9.7bn) deal for Japan to build the country's first high-speed train line, according to reports.