The supermodel - who has previously taken to the stage with former boyfriend Pete Doherty and recorded a duet with Primal Scream - is desperate to pursue her dream of rock stardom further and has asked the 'Not Fair' singer if they can collaborate together.
A source said: "Kate is obsessed with becoming a rock star. She's desperate to persuade Lily to include her on a new album."
The pair have become very close in recent months and Lily is so keen to keep their friendship alive she is willing to let Kate sing on the album, which she is yet to start work on.
The source added: "Lily adores Kate and it seems like she'd do anything she suggests. They say they're like sisters as they've got so much in common."
Kate, 35, is said to be delighted to have found a friend in 24-year-old Lily as she has finally found someone who wants to party as much as her.
The insider explained to Closer magazine: "A lot of Kate's older friends have calmed down, but Lily is as mad as she is when it comes to staying up all night. They just love it."
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