Radcliffe is best known for his portrayal of the titular boy wizard in the Harry Potter film franchise, as well as for his work in the stage drama, "Equus."
If the production gets the green light, Rob Ashford would direct and choreograph it, the entertainment industry trade newspaper said.
The reading reportedly is to take place in December. No other cast members have been confirmed yet, Variety said.
NBC reportedly holds celebs hostage to Jimmy Fallon's show
Ray Liotta sues skin care company over use of likeness