Norton originally wanted the Radiohead frontman to pen about 75 minutes of jazz music for the period drama, which he directs and stars in, but instead turned to Wynton Marsalis, a legend of the genre, to write most of the film's music, with Yorke contributing one track, "Daily Battles".
The "Fight Club" star told The Guardian the pals decided not to work together as the musician felt a little upset with the use of his score in Luca Guadagnino's 2018 film "Suspiria" and he didn't want a similar situation to ruin their friendship.
"Not to say that we don't love Luca," Norton says. "But Thom came off Suspiria feeling so burned."
Explaining the decision to limit their collaboration to one song, he adds: "The last thing you want with somebody you know is to get into a bloody situation. That's the nightmare of all nightmares."
Before turning to Marsalis, the actor and filmmaker sounded out Yorke's Radiohead bandmate Jonny Greenwood, and the composer's longtime collaborator Paul Thomas Anderson.
Yorke nearly worked on another of Norton's films two decades ago - the "No Surprises" hitmaker was offered the chance to score "Fight Club", as co-star Brad Pitt was also a Radiohead fan.
However, explaining why he turned it down, the musician says: "Got the email. Got the script. And I was just too f**ked up in the head to do it."
"Motherless Brooklyn" debuted in cinemas in early November (2019).