Of having four children, a source close to the family tells PEOPLE that Kim Kardashian West "talks about it all the time"

As much as they love being parents, baby No. 4 will “likely” complete Kanye and Kim Kardashian West‘s immediate family.

Following the news that the spouses are expecting their fourth child, via surrogate, a source close to the family tells PEOPLE that their excitement is through the roof.

“Kim has always wanted four kids. She talks about it all the time,” the insider reveals of the Keeping Up with the Kardashians star, 38, who’s already mom to Chicago, 1 this month, Saint, 3, and North, 5½.

However, the source adds of Kardashian West, “She likely won’t have any more after this.”

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The West family
| Credit: Kim Kardashian West/Instagram
KKW Beauty At ULTA Beauty
Kim Kardashian West
| Credit: Stefanie Keenan/Getty Images for KKW Beauty

The source’s remarks echo ones that Kardashian West made in an April cover interview with Elle, explaining that although “my home and my heart feel really full right now,” she wasn’t ruling out another baby — but she was drawing the line at four kids.

“I don’t think I could handle more than that. My time is spread really thin,” the KKW Beauty mogul divulged. “And I think it’s important that in all couples, the mom gives the husband as much attention as the kids.”

Credit: Kim Kardashian/Instagram:=

And though Kardashian West has been candid about her fears surrounding surrogacy and how she thinks it “is so much harder” than pregnancy, she opened up in May about how it ultimately was an overwhelmingly positive experience.

“I would have maybe one more [child],” she admitted. “I really, really enjoyed the surrogacy process. I will say, when it came to the breastfeeding time, I was like, ‘Okay, this is the best decision I ever made.’ ”

Versace show, Arrivals, Pre-Fall 2019, New York, USA - 02 Dec 2018
Kanye and Kim Kardashian West
| Credit: Stephen Lovekin/WWD/REX/Shutterstock

Another source told PEOPLE on Wednesday that, for West, “being a dad is the most important thing that he does, and despite his other problems, he’s an involved, loving dad to his kids.”

“You should see him when he gets around the kids; he lights up. He smiles, he plays with them, he is genuinely excited to be around them and they respond the same way to him,” said the insider.

“They stabilize him,” the source explained of the 41-year-old rapper. “It’s almost like a physical change.”