The US star claims she offered a 40% cut but the band's "relentless" lawyers refused and want all the publishing royalties.
The copyright claim is said to relate to Get Free, from her Lust For Life album.
"Although I know my song wasn't inspired by Creep, Radiohead feel it was and want 100% of the publishing - I offered up to 40 over the last few months but they will only accept 100.
"Their lawyers have been relentless, so we will deal with it in court."
Radiohead themselves were successfully sued over Creep's resemblance to The Hollies' song The Air That I Breathe.
Radiohead had to credit The Air That I Breathe's writers in the notes to their Pablo Honey album and reportedly gave them a cut of the royalties.