The Scottish singer was discovered by the music mogul on his TV talent search show 'Britain's Got Talent' and the singleton joked she would love to tie the knot with the famous bachelor because she knows he would look after her.
In an interview with The Sun newspaper, she revealed: "I'm happier now. I'm not so lonely. I was lonely before I was missing the people close to me. So am I still looking for someone to watch over me? Just Simon Cowell. He's lovely. Marry me!"
Susan also revealed she asked Madonna for permission to feature the song 'You'll See' in the new musical 'I Dreamed A Dream' based on her life, but the Queen of Pop refused.
She explained: "We had to get permission for all of the songs in the show.
"Cameron Mackintosh gave us permission for 'I Dreamed A Dream' from 'Les Miserables' but we never got Madonna's 'You'll See'.
Although Susan, 50, has achieved worldwide fame, she is happiest when at home in her house in Scotland.
She said: "Most folks are great but when someone comes up and sticks their camera phone in your face it's bad manners. It's like you're not a real person, you're a commodity. I went to Ireland once thinking it would be quiet and they were on me like wasps on jam."