The Indian actress, who found fame in Danny Boyle's Oscar-winning Slumdog Millionaire in 2008, has been offered a part in a film being made by the country's prolific movie industry, according to the website Mid-Day.com.
Filmmakers Vikramaditya Motwane and Navdeep Singh have been working on a script and think one of the parts would be perfect for the 28-year-old.
A source said: "Both Vikram and Navdeep felt that Freida would suit the role. She has liked the script and will take a call soon."
However, Navdeep was quoted as saying it was "too early" to comment on whether Freida would be making her Bollywood debut in the movie.
Freida, who is dating her Slumdog co-star Dev Patel, has been in several films since her big screen debut, including You Will Meet A Tall Dark Stranger and Rise Of The Planet Of The Apes.