The Scottish rocker - who is currently touring Australia with the band - is keen to develop a stage show, based on an unnamed modern celebrity.
He said: "I did have this amazing idea, I've been keeping it a secret for ages! I think it would make an amazing musical.
"The thing is, what would make a great musical would be to pick a contemporary figure, like somebody from either current times of the last 10 years. Somebody who's had a big impact. And write it about them."
Alex added, however, that he has not started the actual writing of the musical - although he has a person in mind whom he wants it to be about, although he would not reveal their name.
Last year, Alex revealed Franz Ferdinand turned down the opportunity to play in front of the British royal family, after they were requested by Prince William for a Royal Command Performance in 2004.
He said: "I've nothing against Prince William personally and I appreciate the fact that he's a fan of the band, but ideally, musicians belong outside the establishment.
"When they cross that line, it's like something in them has died. Hanging out with the Royal Family is simply not a very Franz Ferdinand thing to do."