"Kim still seems concerned but is supportive. They don't know for how long Kanye will need outpatient care," a source told People, describing Kardashian as "overwhelmed".
The award-winning musician was hospitalised on November 21 suffering from "temporary psychosis due to sleep deprivation and dehydration", TMZ said.
The Los Angeles Police Department (LAPD) said at the time that it responded to a report of a disturbance but the incident was deemed a "medical emergency".
Dr Farzam told police that West had attempted to assault a gym staff member and he was placed in an involuntary psychiatric hold, known as a 5150, meaning he was handcuffed to the stretcher as he was taken to hospital, according to TMZ.
West's admission to hospital came a day after his Saint Pablo tour was cancelled following a series of onstage outbursts, a month after Kardashian was tied up, threatened with a gun and robbed in Paris, with the traumatic ordeal reportedly haunting his dreams.
The stress of the pair's never-ending $11 million house renovation project has also been cited as a potential contributor his mental health struggles.
The award-winning singer ended a concert after four songs in Sacramento, California, before cancelling a performance in Los Angeles a day later, just hours before he was due on stage.
He had previously spent 10 minutes ranting about Beyonce, Jay Z, Hillary Clinton and Facebook founder Mark Zuckerberg during another show.
He was also heckled by concertgoers after telling them he would have voted for Donald Trump in the US presidential election had he decided to cast a ballot.
Model Kendall Jenner, the half-sister of Kardashian, said the family had been praying for West as she spoke to reporters at the Victoria's Secret fashion show in Paris on Wednesday.
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