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Lauren is believed to be around ten weeks along and she is also still married to Simon's pal Andrew Silverman.
Although Simon refused to be drawn on the speculation when he was filmed leaving The X Factor studios in Los Angeles last night, a friend of his has insisted he will do the right thing.
"Simon has given all his exes houses - so of course he's going to be generous to his own child. He has not even considered not looking after this baby," the insider told MailOnline.
"Anyone who knows him knows that he's generous to a fault. Lauren keeps saying that she just wants to be with him, she's so in love with him, they're very good together. She makes him relax and have fun.
"She's fun loving, she loves a party and a giggle. Simon's himself around her, she's been good for him. He's so happy."
Lauren was seen for the first time since the story broke today. The 36-year-old was pictured walking with her seven-year-old son Adam near their New York home. She was dressed in a baggy white shirt and black leggings, with a small baby bump seemingly apparent.
Today it was revealed that Andrew has named Simon in divorce papers he filed two weeks ago. He is asking to end the marriage due to adultery.
"It's a very unusual thing to name him. And considering they are all supposed to be friends it's a very unusual step to take," divorce lawyer Vanessa Lloyd Platt told MailOnline.
"Andrew would have not only had to name him, but Simon would also have had to be served with the papers. It's all going to very muddy, muddled and an absolute nightmare for Simon."
Another friend has claimed Andrew only took the steps because he wanted to embarrass music mogul Simon in public.
"This is just to exact revenge," the source claimed.
Simon is said to be "freaked out" by the news he is to become a father although he knows the child is his. His mother has spoken of what a great dad he will be, but his ex-girlfriends are said to be less impressed.
Former pop star Sinitta has dated the star on-and-off for 20 years and is said to have cried when she heard the news and said it "should have been her". Terri Seymour has given the pregnancy her blessing, while Simon's former fiancée Mezhgan Hussainy is in a state of shock.