"No one is worried about anyone stealing their thunder," a source tells PEOPLE of Kim Kardashian, Khloe Kardashian and Kylie Jenner

Kim Kardashian West is “excited” that her sisters are pregnant, and hopes that the next generation of their family is as tight-knit as they are, a source close to the reality star tells PEOPLE.

While Kardashian West officially confirmed her own exciting baby news in a supertease for the upcoming season of Keeping Up with the Kardashians, she’s not the only one who’s growing her family — sisters Kylie Jenner and Khloé Kardashian are both pregnant.

PEOPLE previously reported that the reality star mom, 36, and husband Kanye West had hired a surrogate in June and earlier this month it was revealed that the surrogate is pregnant. (The couple are already parents to son Saint, 21 months, and daughter North, who turned 4 in June.)

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A close family insider tells PEOPLE that the family baby boom is welcome news for Kardashian West. “There is no jealousy here,” the source says. “No one is worried about anyone stealing their thunder. It’s not dramatic like that.”

In fact, the source says that Kardashian West and West, 40, are thrilled at their growing extended family. “I think Kanye is even more excited,” says the source. “He was an only child; he didn’t have a bunch of kids around. He’s been very honest about how lonely that could be for him.”

Continues the source, “And now there will be three siblings, along with a huge extended family. This sounds like a dream come true for him.”

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“Kim is really into the idea of a bunch of babies being born around the same time,” the source continues. “She think they’ll be more like sisters than cousins. Everyone in the family is just thrilled about the whole thing.”

That’s not to say that Jenner’s pregnancy didn’t catch everyone off guard. “No one was thrilled about Kylie because she’s so young and naive,” the source says, “but everyone has come around and they are focusing on the baby.”

“They truly believe that Kylie will rise to the occasion and be a good mom,” adds the source of Jenner, 20. “And they’ll be there to help!”