The Saawariya director is pairing up with his art director Omung Kumar for the project.
He told The Times of India: "Omung brought the script to me a month before the Olympics. Mary Kom has made India proud. I was moved by her story.
"She is a mother of two, has been through so much struggle, has tremendous spirit and a sense of living and dignity and is now a World Champion. She has what it takes to make a great champion.
"An Indian woman boxer is rare. It will be an exciting film to produce and I am very happy to do it."
Kom won a bronze medal for India in the 2012 Summer Olympics, which was the first to feature flyweight women's boxing.
The director's most recent release was the box office hit Rowdy Rathore starring Akshay Kumar and Sonakshi Sinha.
Bhansali is currently working on an adaptation of Romeo and Juliet titled Ram Leela.
Watch the trailer for Rowdy Rathore below: