The couple was reportedly spotted together in France last month, holding hands and enjoying time together.
"Simon very much enjoyed their vacation," the source added. "The baby is bringing him and Lauren even closer -- it's just amazing to see Simon this happy. Lauren and the baby have really changed his life for the better."
According toUs Weekly, Cowell, 53, and Silverman, 36, have known about their baby's gender for awhile now and caught a glimpse of the child in a recent sonogram.
"You literally see this thing which is now alive moving around," Cowell, who previously judged American Idol with blunt honesty and often harsh criticism, reportedly told the Times of London on Monday. "I feel very paternal right now. So I am very happy. [But] I can assure you: I won't go soft."
Silverman, a New York socialite, is pregnant with Cowell's child as a result of an "adulterous affair" that ended her marriage to "estranged" husband Andrew Silverman, who was Cowell's former close friend.
While Cowell also told BBC News late last month he's "proud to be a dad," according to a previous New York Daily News report, he originally felt blindsided and "tricked" by the news he and Lauren are expecting a child together.
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