Cowell previously touched on the topic of baby names and dropped a couple possibilities during a recent interview with Extra.
"My number one choice is Simon because I like the name," the 54-year-old joked, adding that his second choice would be Eric after his father.
"His birthday is going to be very close to my dad's birthday."
While Cowell told Extra he "really would like the idea of teaching him how to run the business," he also told E! News he can't wait to show his son "how to drive racing cars" one day.
"We'll wait until he's 2 years old," Cowell joked.
Cowell, who reportedly claimed he's "useless" at parenting basics such as how to install a car seat, he insisted, "I'll get there."
He certainly does, however, want to be a pretty laid-back Dad and not obsess about how a child could or should be raised.
"Be cool about it, and don't worry about things to much... the way my brother and I were brought up, it was kind of relaxed. There were no self-help books," the music and television producer told Extra.
Silverman, a 36-year-old New York socialite who's reportedly expecting Cowell's baby early next year, was still with ex-husband Andrew Silverman when news of the pregnancy first surfaced in July.
The "adulterous affair" ended the couple's marriage and led Andrew, Cowell's former close friend, to file for divorce on July 15 -- citing adultery and naming Cowell a co-respondent. Lauren and Andrew have since reached a divorce settlement out of court.
"Let's put it this way, I wouldn't expect her to be a single mother," Cowell reportedly told Ryan Seacrest during an appearance on his On-Air with Ryan Seacrestsyndicated radio show.
The X Factor's third-season Top 12 performance show will air Wednesday night at 8PM ET/PT on Fox and be followed by a results show on Thursday night.
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