The 31-year-old singer was approached by the chart-topping group to sing on one of their tracks but she ''wasn't into'' the music.
Speaking with the Daily Star newspaper, Clean Bandit singer and cellist Grace Chatto said: ''I have tried to get her to sing on one of our songs but she wasn't into it...''
The 'Solo' hitmaker once admitted that although a fan of her voice, Ellie's music was not to her taste at first.
She said: ''I'm obsessed with her voice, although at first I wasn't into her music.
''But then 'Love Me Like You Do' came out and I became obsessed.
''There is something really addictive about her voice.''
Jack Patterson, the 33-year-old bassist of the trio, is currently working with Jess Glynne on music for her album- and the band are keen to keep working with even more UK artists.
Grace revealed: ''We've done another song with Anne-Marie that will probably be on our album. It's really beautiful and is called 'Should Have Known Better'.''
Ellie, meanwhile, has been spending time in the studio with English DJ and record producer Jax Jones and has been loving the advice the 'Love Me Like You' star has to offer.
Jax previously said: ''I've been learning more about the environment from Ellie Goulding.
''We did a session and she has been teaching me all about global warming.
''She has taught me a lot about the work she does for the UN and humanitarian stuff.
''I can now say it has become more of a passion.''