The former 'Britain's Got Talent' winner wanted to feature the singer's hit 'You'll See' in the forthcoming show about her rise to fame, titled 'I Dreamed A Dream'.
But while she got the go-ahead to use the song of the same name from 'Les Miserables', 50-year-old Susan says Madonna was not so forthcoming.
She said: ''We had to get permission for all the songs in the show.
''Cameron Mackintosh gave us permission for 'I Dreamed A Dream' from 'Les Mis' -- but we never got Madonna's 'You'll See'.''
But she insists the production is just as powerful without it - in particular the part where doctors tell her parents Patrick and Bridget that a new-born Susan has been deprived of oxygen.
Attending the show's rehearsals in Glasgow, she told The Sun newspaper: ''Why do I cry at that? Because that's the reality.
''That's when the doctor tells my parents, 'Don't expect too much.' He prejudged me. All the doctor told my mum was what I wouldn't be able to do, not what I could do.
''But my dad said, 'All that child needs is love -- and we've got plenty of that'. It makes me cry just thinking about it, never mind seeing it on stage every night.''
She continued: '''I Dreamed A Dream' is a very romanticised view. It's more like I dared to dream -- that's what it feels like to me.
''Because everyone dreams of changing their circumstances, though not in the way I did. I couldn't have imagined taking off the way I did.''