EXCLUSIVE: Kanye West 'Misses His Kids,' Remains Hospitalized With Kim Kardashian by His Side

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Amid Kanye West's ongoing hospitalization, the rapper seems to be missing his children.

"They are not sure when Kanye will be released and get to go home," a source tells ET on Wednesday. "It changes day to day, which has been very difficult for Kanye and for Kim."

By Kanye's side is his wife, Kim Kardashian West, who remains devoted to supporting her husband "24/7." As ET previously reported, Kanye remains in an area of UCLA Medical Center that does not allow for extended visitors. Though the couple's children, 3-year-old North and 11-month-old Saint, are allowed to visit with adult accompaniment and patient permission, ET's source does not believe that North and Saint have done so.

WATCH: Kanye West Still Hospitalized After One Week - Where Things Stand 

"He would love to be out there as soon as possible and just get home to his family," the source says. "He misses his kids."

Kanye was hospitalized last Monday after what one source described as "a mental breakdown" and another attributed to "sleep deprivation and exhaustion." After one week in the hospital, as ET reported on Monday, the 39-year-old superstar allegedly remained undiagnosed by doctors. According to a source, Kanye had suffered from "severe paranoia" and "hallucinations" brought on by a "lack of sleep" associated not only with his intense workload, but also with stress from Kim's horrifying armed robbery in Paris last month.

"Kim is still by his side, 24/7," a source now tells ET, speculating that Kanye could remain hospitalized for a "few more days."

"She will not leave the hospital until Kanye does," the source adds.

A source previously revealed to ET that Kim had been seriously "stepping up" for her husband at this difficult time, claiming that the 36-year-old reality star is "more dedicated and devoted to Kanye than ever." The source even went on to say that the situation has made the couple's marriage stronger.

"She knows that there are limitations for how much a person can do or take on," the source said. "She knows that he just needs a break, and she will make sure he gets that."

For more on where things currently stand with Kim and Kanye -- and what this all means for Keeping Up With the Kardashians -- watch the video below.