After targeting Miley Cyrus in an open letter last week (ends04Oct13), O'Connor turned on Cowell and his X Factor sidekick Louis Walsh, blaming them and their singing competition programmes for the alleged downfall of the music industry.
In an interview on The Late Late Show, she told host Ryan Tubridy, "I feel sorry for the murder of music and rock 'n' roll, which has happened because of the industry. Because of Simon Cowell, Louis Walsh. They've murdered music. I stand to say it on behalf of every musician in the world and they'll agree with me,"
"The industry has taken over so much, the money-making side of it, that the sexualising of extremely young people making records, and all the worship with money and bling and diamonds... it all amounts to the murder of music and that's what concerns me."
Cowell has now responded to the singer's Tv outburst, but rather than attacking her for making the remarks, he has invited her to attend a taping.
Taking to Twitter.com, he writes sarcastically, "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."
This isn't the first time Cowell has invited a celebrity critic to come on the show - in 2009, Sting called The X Factor 'appalling' and 'televised karaoke', to which the Tv judge welcomed the singer to 'impart his knowledge' on air.
Last week (begs30Sep13) the Nothing Compares 2 U hitmaker hit the headlines after penning an open letter to Cyrus, suggesting she refrain from stripping off, dancing provocatively and "prostituting" herself in performances and music videos.
Cyrus responded by first poking fun at O'Connor's past mental health issues and then suggesting the two singers arrange to meet and chat. The Irish star responded by threatening legal action against the 20 year old for her mockery.