According to The Sun, the singing duo could feature as themselves in an episode of the animated sitcom.
A Fox spokesman said: "Castings are not something we can talk publicly about, but we are taking a look at the boys.
"We love anything Irish - we set a whole show there last year. They are certainly charming and good-looking fellows."
Edward said: "We would love to be on The Simpsons. John, Edward and the Simpsons - we're best friends with Bart!"
Britain's Got Talent star Susan Boyle was namechecked by Homer Simpson in an episode of the Sky1 show earlier this year.