The rocker's wife Ashlee Simpson-Wentz has revealed 14-month-old Bronx has already started listening to the group and some of his mother's pop hits.
She said: "He's definitely heard Fall Out Boy and my music, too, but we play everything for him. He gets to choose his own kind of music, but he doesn't have a favourite yet."
Ashlee, 25, insists she and Pete would be pleased if their son decided to follow in their footsteps and entered the music business.
She added: "It's definitely not something I'd push on him - I want to let him be whatever he wants to be - but we'll see."
However, Ashlee tries to keep Bronx away from the glare of the paparazzi as much as she can at the moment.
She said: "We don't want to raise him in the spotlight. We try to keep our life as private as we can. I think he's just starting to notice them (paparazzi). It's more frustrating for Pete and me - Bronx doesn't quite get it!"