The music mogul and his partner Lauren Silverman have asked singer Sinitta - who previously revealed she aborted the 'X Factor' boss' baby in the 1980s - to look after the spiritual welfare of six-week-old Eric.
Posting a photo of herself cradling the baby on twitter, she wrote: "
"Wanted you to be the first (well after my mom and children) to hear about my next, serious new role... Drum roll...
"At Mothers Day lunch with Mom, Magdalena, Zac, @JasonJGale @SimonCowell I was asked to be godmother to Baby Eric!!! X (sic)"
Sinitta - who chose Simon to be godfather to her children Magdalena and Zac - has remained close to the 54-year-old star and previously admitted she felt "betrayed" when she found out he was to be a father.
She said in September: "I was completely and utterly stunned. I was in such a daze, to the point where I wondered if I was dreaming it.
"We knew we were all close friends but I didn't realize he and Lauren were falling in love and, when I found out, I will admit I was taking aback and did feel a sense of betrayal"