Chris Weitz also revealed at the Comic-Con convention in San Francisco that Bon Iver would feature on the score.
The film, which stars Robert Pattinson, is due to be released in November.
"I selfishly want to put songs in by artists I love - and some the cast and crew also happen to love," Weitz told HitFix.com.
"I think [Bon Iver] is fantastic. He says he wrote it for the film, but who ever knows if it might just be something laying around in his cupboard.
Weitz, who first mentioned Yorke's involvement during an interview earlier this month, said he hoped to listen to the Radiohead singer's contribution today.
"Unless it's sounds of him belching, I think I'll put it in, he joked.
Meanwhile, the director also confirmed that he is "hoping to get Kings Of Leon to contribute to the soundtrack.
As Gigwise reported last week, the band's frontman Caleb Followill said in a recent interview that he was too busy to write a song for the movie.
New Moon is the second part of the four-part Twilight Saga, which tells the story of a vampire who falls in love with an ordinary schoolgirl.
The soundtrack to the first film featured songs by Muse, Paramore and Pattinson.
Thanks for the report to Gigwise.com.