"If the fairies are with us, I'd like to say that before the end of 2013 it will be playing at the National."
It was announced last year that the show, scheduled to open in April 2012, had been postponed. Amos said the project was still at the workshop stage.
The Light Princess, which the American singer-songwriter has been developing for several years, is based on George MacDonald's 19th Century fairy tale.
Amos, 49, said it had been "a great challenge" marrying the fairy tale element with a 21st Century story that resonated with the teenage girls and young women of today.
Sir Nicholas Hytner, the National's artistic director, had been the "driving force" and her mentor on the project, the singer continued. West Side Story, she said, had been a "big influence" on her musical. "We've been spending the last year getting it to a place where we're feeling really good about it," she added.
MacDonald's 1864 fairy tale tells of a princess who, having been cursed by a spiteful aunt, defies gravity and floats away unless she is in contact with water.
She tries to master the art of crying so that she can marry a prince who has fallen in love with her.
Amos shot to fame in 1992 with her album Little Earthquakes and has since sold more than 12 million albums worldwide. She is about to release Gold Dust, an album of reworked, orchestral versions of songs from her 20-year back catalogue.