The couple - who are expecting their first son - had been spotted having what seemed to be an argument in their SVU on Thursday and it is said it stemmed from the media mogul having a jealous side.
A source told RadarOnline.com: "I heard Lauren say, 'Trust issues...You're talking about trust issues?!'"
It follows reports the US socialite has been growing tired of Simon staying close to his ex-girlfriends - including Mezhgan Hussainy, Sinitta, Jackie St. Clair and Terri Seymour - and the situation is said to be a "dilemma" for the X Factor boss.
An insider previously said: "Lauren's told him she wants to be in a normal relationship, without the other women hanging around.
"She also thinks that Mezhgan has been making more of an effort with her appearance lately and Lauren's told him he's got to get her off the scene.
"It's a big dilemma for Simon as he doesn't like being told what to do and loves Mezhgan's company, but he's serious about wanting to make a go of things with Lauren and the baby."
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