The father-to-be shared his preferences with Extra presenter, and former flame, Terri Seymour.
"My number one choice is Simon because I like the name," the 54-year-old revealed, with tongue in cheek.
Simon is expecting his first child, a baby boy, with Lauren Silverman
He said that his second favourite for his first child with Lauren Silverman is Eric, after his late father, who passed away in 1999.
"His birthday is going to be very close to my dad's birthday," Simon said of his baby son, adding that his own father would be "very proud" and "amazed" to have a grandson.
The X Factor judge also said that he wants to adopt the same parenting style with which he was raised.
"Be cool about it. You know, don't worry about things too much, " he said. "The way my brother and I were brought up, it was kind of relaxed. There were no self-help books or any of that crazy stuff."
Simon pictured with his mum Julie and brother Nicholas
Simon went on to say that he was looking forward to having his son follow in his footsteps.
"I want to teach him how to do my job as quickly as possible," he joked. "I want to pass the reins over. I really like the idea of teaching him how to run the business."
It's not the only thing Simon is looking forward to teaching his son.
"I'm not brilliant with babies. I never know what to do. But once he's older I think I'll be a good dad in terms of advice," Simon said in a recent interview with Parade magazine.
"And then I'll get to do all the things I want to do, like go to Disneyland or Universal Studios, teach him how to drive — I love all that."