Brie Larson, the star of Room, the drama which has won the prestigious People’s Choice award at the Toronto film festival, is in talks to replace Emma Stone as Billie Jean King in forthcoming film Battle of the Sexes.

The film, which will be directed by Little Miss Sunshine team Jonathan Dayton and Valerie Daris, from a script by Simon Beaufoy, is due to shoot later this year. Stone was attached to the project, but has now dropped out because of a scheduling conflict.

In 1973, King, then 29 and world No 2 female tennis player, was challenged to a match by Riggs, the 55-year-old retired former Wimbledon champion. She accepted and it was played in Houston, with a $100,000 prize and much pageantry.

King was carried into the Astrodome on a throne held by four muscled men stripped to the waist, while Riggs followed in a rickshaw drawn by lightly dressed models. Riggs gave King a giant lollipop. She presented him with a – live – piglet.

It is the third film in development about the clash: Elizabeth Banks and Paul Giamatti are lined up for an HBO production, while Will Ferrell is attached to a competing title called Match Maker.

Larson is tipped for an Oscar nomination for her role as Ma, a woman kidnapped, raped and held captive in Room, Lenny Abrahamson’s adaptation of the Emma Donoghue bestseller. Earlier this year she played Amy Schumer’s sister in Trainwreck, and will also be seen in monkey horror Kong: Skull Island.

• This article was amended on 21 September 2015. An earlier version said Brie Larson played Amy Poehler’s sister in Trainwreck. Larson played Amy Schumer’s sister in the film.