The 54-year-old 'American Idol' judge apparently got emotional and wanted to be together soon after his son was born, reported E!Online.
"It's a happy time. They're settling into their new life," a source said.
However, the couple are not planning to have any engagement soon and is currently enjoying the happy phase.
Cowell had earlier said that he was born to be a father during his first post-baby interview.
"I was born to be a dad. I wouldn't rule out [more children]. I had a brother when I was younger, so I kind of think it's cool to have two or three...Two," he had said.
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