The stage show, which had been due to open for previews this week, is a parody of The X Factor and was written by comedian Harry Hill.
Although Simon hasn't given away the exact details as to why Cheryl is likely to be fuming, he is pretty sure of her reaction!
In an interview with The Sunday Times' Culture supplement, Simon said: "Cheryl is going to kill me when she sees it. I mean, seriously, I'm going to get it in the neck."
Simon, who is played by former EastEnders star Nigel Harman in the musical, also admitted that The X Factor had previously turned down offers for a serious stage show based on the TV programme.
"We had lots of people trying to do really serious versions of the show, but we just turned them down," he added.
"When Harry used to take the p*ss out of us on TV Burp, we all wanted to be the one he parodied."
Unfortunately, although people are lining up to get tickets for 'I Can't Sing', the first two shows have already been cancelled.
On Thursday and Friday of this week, critics and theatre-goers were due to watch a preview of the musical. However, "technical difficulties" mean the shows are now no longer taking place.
Rebecca Quigley, producer for Stage Entertainment, said: "After much careful thought and discussion we've decided that we need to take some more time to work on technical aspects of the production.
"As audiences will soon see the production is hugely ambitious, and the volume of installation and scale of the set means that technical work has taken slightly longer than could have been anticipated.
"This is not a decision taken lightly and I'd like to apologise to those who had booked, and indeed sold out, these initial two performances."
Do you want to see 'I Can't Sing'? Tell us below, as the best comment from across the website each week wins £50.