According to The Sun, friends said: "Simon's made it clear he'd like Eric to be considered as a name."
The X Factor mogul's three months' pregnant lover Lauren Silverman, 37, is also said to be keen.
"Lauren likes it as it's unusual in America, and quite stylish too," said the paper's source. "She also feels Erica's a cool name for a girl."
Record label executive Eric died of a heart attack in 1999, aged 81.
Simon has admitted: "My dad was a brilliant mentor."
Love the idea of baby Eric!