According to The Sun, Cowell has sent his executive producers in hot pursuit of the star, who is currently writing the score for Bridget Jones The Musical.
A source told the newspaper, 'Lily was flattered to get Simon's call. It's a big job and an honour to be asked. But she's not convinced.
'She has tried to take a step back from the limelight over the last six months and doesn't want to be thrust right back into the madness of the showbiz pantomime that comes with the show.
'She doesn't need the money or the hassle at this stage in her life. Maybe in a few years' time when circumstances change she will be more receptive.'
The 25-year-old has won three Ivor Novello Awards for her song writing, and Best Female at last year's Brits.