The production will focus on the boy wizard's early years and his parents' backstory, rather than a new version of the books and films, reported Daily Mirror.
In Rowling's books, Harry's parents are killed by Lord Voldemort when he is just 15 months old.
Tiffany is Rowling's first choice as director, after he staged the current West End version of 'Let the Right One In'. His recent credits also include 'Black Watch' and 'Once'.
Writer Jack Thorne and producers Sonia Friedman and Colin Callender are also linked with the production.
This is the latest Harry Potter spinoff in recent months from Rowling, after she published match reports from the Quidditch World Cup, and announced three movies based on 'Fantastic Beasts and Where to Find Them'.
