Just a week after the birth of their third child, Kim Kardashian West is already thinking about another baby.

"Even before Chicago was born, Kim was talking about asking the surrogate to carry her next baby," a source tells PEOPLE.

The couple welcomed their second daughter Chicago on January 15 by surrogate. After Kim carried their first two children, North who is four, and Saint who is two-years-old, she was warned of health concerns in future pregnancies.

"I have always been really honest about my struggles with pregnancy. Pre-eclampsia and placenta accreta are high-risk conditions, so when I wanted to have a third baby, doctors said that it wasn't safe for my"”or the baby's"”health to carry on my own," she said.

That's when the family turned to a surrogate to carry their third child.

"We are incredibly grateful to our surrogate who made our dreams come true with the greatest gift one could give and to our wonderful doctors and nurses for their special care," she said.

But it turns our their surrogate's work may not be done.

"She's so happy with the whole process and thrilled with the surrogate," says the insider, adding of the expectant father, "Kanye was even bonding with the surrogate's husband in the delivery room."

While referring to the woman as her surrogate, she clarified that she is actually the family's gestational carrier.

"A traditional surrogate donates her egg, is artificially inseminated with the father's sperm and then carries the baby to term," Kim said.

"Since we implanted my fertilized egg in our gestational carrier, our baby is biologically mine and Kanye's," she confirmed. Adding: "You can either choose someone that you know or you can go through an agency, like Kanye and I did."

The family is said to be bonding, and that is making Kim want to further expand their brood.

"Kim definitely wants more kids. She is so happy being a family of five. She wants the family to get even bigger!"

Kayne seems to be on board as well.

"It's true that he was really the push for baby No. 3 because he loves kids and wants a lot."

Kim responded to the claims with a tweet.

What do you think? Could their be a fourth baby on the way?

Source: People