Rapper Jay-Z is writing some music to be featured in the contemporary big-screen remake, while Smith's father, Will, is producing the picture.
"I have been writing the script for nearly three years; it's exciting," Thompson told the BBC.
"In the autumn, we get to go to Los Angeles to work with Willow and work on more of the script," said Thompson. "Jay-Z has already started working on the music. We will start shooting in the spring in New York."