Danny Boyle has been tipped to take on a biopic of Billie Jean King which would centre on the the tennis champion's infamous "battle of the sexes" match against male veteran Bobby Riggs.

The New York Post's Page Six column reports that Boyle is currently in the Big Apple for talks with King and other proposed participants. The Oscar-winning Slumdog Millionaire screenwriter Simon Beaufoy, Boyle's regular collaborator, is said to be in charge of the script.

King's battle with Riggs in 1973 still stands as one of the most watched tennis matches of all time. It took place after the 55-year-old former Wimbledon and US Open winner challenged the reigning women's Wimbledon champion to a high-profile televised match in Houston, Texas, insisting he would emerge victorious despite the 26-year age gap between the participants.

King won in three sets, 6-4, 6-3, 6-3, after nullifying her opponent's tricky drop shot and lob-based game by playing defensively from the back of the court. Riggs had earlier defeated the women's No 1, Margaret Court, using similar tactics.

The story, which was previously brought to the big screen in a 2013 documentary by James Erskine, is ripe with further intrigue. Persistent rumours – always denied – suggested Riggs might have thrown the match to pay off gambling debts to the mob. But contemporaneous observers said the famously competitive veteran was so upset following his defeat that any such reports should be dismissed out of hand. Had he won, Riggs's next match would have been a battle against Chris Evert on clay for a $1m prize.

Boyle was spotted at the London premiere of Erskine's documentary, titled The Battle of the Sexes, last year, sparking rumours that he might be interested in a dramatic version.