EXCLUSIVE: Kanye West still hospitalized and undiagnosed, Kim Kardashian remains 'by his side 24/7'

It's been one week since Kanye West was admitted to UCLA Medical Center, where he remains hospitalized as wife Kim Kardashian West vigilantly supports him, a source close to the couple tells ET.

According to the source, the initial plan was for Kanye to leave the hospital on Monday, though the decision was tentative depending on his doctors' decision. The source says 39-year-old Kanye has not been diagnosed with anything specific.

"Kanye's doctors are super reluctant to diagnose anything, mainly because a mental or cognitive disorder cannot be diagnosed after one hospital visit, but rather after observing someone's behavior over the course of a specific time frame," the source explains. "Kanye is there in the hospital because he knows he needs to get better and he wants to get better."

See photos of Kanye West and Kim Kardashian together:

NEWS: Inside Kim Kardashian and Kanye West's Marriage -- How They Support Each Other, Even When Times Get Tough

Through it all, 36-year-old Kim has faithfully remained by her husband's side "24/7," the source also shares.

"Kim is more dedicated and devoted to Kanye more than ever," the source says. "She knows that there are limitations for how much a person can do or take on. She knows that he just needs a break, and she will make sure he gets that. This is only making their marriage stronger."

"Kim is the type of person who steps up in these kinds of situations," the source adds. "She stays so calm, collected and takes control. This is the perfect scenario for her to really make a difference for Kanye. She's been incredible."

On Thanksgiving, Kanye remained in the hospital, where Kim spent time with him, but she also popped in at her family's holiday dinner held at her sister Kyle Jenner's home in Calabasas, California, the source says.

Still, Kanye wasn't far from the famous family's mind. "The entire Kardashian family is very worried," the source says.

WATCH: Kanye West's Hospitalization -- 5 Things We've Learned So Far

On Wednesday, a source told ET that the "Fade" rapper was "doing much better" after being hospitalized. "He just needed some rest," the source said. "[Kim] is currently with Kanye right now at his side. Kim feels more connected to Kanye than ever. Their marriage is doing great."

A source close to Kanye previously told ET that the rapper was battling sleep deprivation and exhaustion and just needed rest. However, another source claimed that Kanye suffered a "mental breakdown" due to his schedule and personal stress. The father of two had been making headlines for erratic behavior during his latest stops on his Saint Pablo Tour, before canceling his remaining tour stops last Monday.

"It was a combination of a lot of issues: stress, anxiety, paranoia. He just broke," the source said. "There have been signs recently of him just overwhelmed. Kanye hasn't been himself for a while."

Watch below:

-- Additional reporting by Jennifer Peros