"Discussions are still fluid. We are expecting the deal to get closed this week," the report said.
Aston Martin, made famous by its cars in James Bond movies, is owned by Kuwait-based finance firm Investment Dar, which bought it from Ford Motors for $767 million in 2007.
But analysts say the global economic slowdown has affected its sales.
Mahindra is likely to pick up a 40% stake initially at a cost of $190-320 million, but could raise its stake to 50% over the next four years, the report said.
Mahindra officials were unavailable for comment.
The other serious bidder, Investindustrial, bought a stake in Italian motorbike maker Ducati Motor in 2006.
Aston Martin, which announced its entry into India in April 2011, expects to sell a quarter of its cars to Asian and Middle Eastern countries in the next five years, its sales director Bill Donnelly told reporters at that time.