Simon Cowell is thinking of naming his baby Ericafter his father, feeling the name would be a fitting tribute to his parent, who passed away from a heart attack in 1999, aged 81.
A source told a UK newspaper: "If it's a boy, Simon wants to call him Eric and if it's a girl Erica.
"His dad meant the world to him and Simon feels the name would be a fitting tribute.
"Lauren has not decided yet, but is taking Simon's input very seriously.
"She likes the name Eric as it is unusual in America and quite stylish.
The source also told the Daily Star newspaper:"She also feels Erica is a cool name for a girl."
Eric worked for music label EMI and helped Simon land a job in the post room, from which he worked his way up to eventually head up 'The X Factor' and appear as a judge on 'American Idol', making him one of the most recognisable faces on the TV in the US and UK.
Simon, 53, previously called his dad a "brilliant mentor," while his mother, Julie, has said "he still misses him terribly".
Meanwhile, Simon is said to be getting used to the idea of becoming a father and has been joined on his yacht near St Tropez, France, by Lauren, 36, who is believed to be around three months pregnant.
A source said: "This is something Simon didn't ever expect to happen ... Now it has, he wants to grab the opportunity with both hands and be a proper dad.
"He wants to be a good dad, just like he regards his own father ... He wants to emulate what his parents did for him."
Tagged in Simon Cowell Lauren Silverman