updated 06/20/2013 AT 11:20 AM ET
•originally published 06/20/2013 AT 12:05 PM ET
Kanye West is taking his daddy duties very seriously.
“Kanye hasn’t left Kim and the baby’s side,” a source close to Kardashian, 32, tells PEOPLE. “He’s been in the room for days making sure everything is perfect for the two of them.”
With her boyfriend there, the usually open Kardashian – who was admitted to the hospital with medical complications on June 14 – is savoring her privacy.
According to a source, “Kim is being very protective of the baby.”
With Reporting By JENNIFER GARCIA
[RELATED_TEXT “More On Kim Kardashian: