The 54-year-old music mogul took to Twitter to appeal to the star to appear as a panellist on the talent show, just days after she declared Simon and fellow judge Louis Walsh have "murdered music" through 'The X Factor'.
He tweeted: "I think sinead o'connor would be a real fun guest judge on X factor. She loves the show and everything I do. Let me know sinead. (sic)"
She said: "I don't feel sorry for me or for anybody else in the matter, that's not what it's about. The broader issue, I feel sorry for the murder of music. I feel sorry for the murder of rock 'n' roll which has happened because of the industry. Because of Simon Cowell, Louis Walsh and the lot of them [talent show judges] have murdered music.
"They're murderers of music! I stand and say it on behalf of every musician in the world and they will all agree with it. I don't give a s**t if I hurt them ... All the sexualisation of young people, all the worship of bling and money and diamonds and 'Pop Idol' stuff, Simon Cowell - it all amounts to the murder of music."
However, in 2009 Sinead said that she would compete on the 'X Factor' if she was trying to break into the music industry.