The British rockers' lawyers are in negotiations with the 32-year-old star's team in the hope of resolving an issue centred around the similarities between their classic 1993 single 'Creep' and her track 'Get Free', which appears on her latest album 'Lust for Life', but will take the battle to court with a copyright infringement lawsuit if the dispute can't be resolved.
A source told the Sun on Sunday newspaper: ''Both teams are trying to thrash it out behind the scenes to prevent it from going to court.
''It's understood that Radiohead's team are hoping for the band to either receive compensation or be credited on the list of songwriters to receive royalties.''
The track is currently credited to Lana, Kieron Menzies and Rick Nowels.
She previously said: ''I was definitely nervous.
''She got off the plane at 10.30, so she didn't get to the studio until midnight - and she just breezed in, black on black, gold everywhere. She was kind of a vision.
''When she started singing, she told me she wanted to hear me sing something, too. And then I really freaked out!
''I said to her over the mic, 'I just sound so quiet compared to you.' And she was like, 'That's OK, you can be my little echo!'
''I thought that was so cool. I'm not as loud as her. My voice isn't as low as hers. But she loves it for what it is.
''That, as it was happening, was a career-defining moment for me.''
In honour of the arrival of the royal baby...
The Vanity Project reveal the truth about their unique aesthetic.
ATR hit Islington's O2 Academy tonight to fully display their importance to thrilling effect.
These artists are no-one's guilty pleasure.
Rocks was released on this day (May 3) in 1976.
Daughters in the current climate are stronger than ever following last year's You Won't Get What You Want.
Je t'aime Taylor Swift's latest video for her new single 'Me!' featuring Brendon Urie of Panic! At The Disco.
Celebrating the wonders of Jazz music.