The 39-year-old rapper was admitted to the UCLA Medical Center in Los Angeles, California, last week for exhaustion and sleep deprivation but was expected to get out yesterday, but it is not now known when he might be able to go home.
According to TMZ, sources with direct knowledge of the situation told the gossip website that Kanye - who had to cancel the remaining dates of his 'Saint Pablo Tour' as a result of his hospitalisation - has not yet recovered enough for him to be allowed home.
When he is released, the 'Flashing Lights' hitmaker's personal doctor will take care of him.
Kanye's wife Kim Kardashian West - who he has three-year-old daughter North and 11-month-old son Saint with - will also help him as much as possible as she has done while he has been in hospital, lying by his side and even feeding him at times.
A source recently said: "Kim has been amazing. She knew he couldn't keep going the way he was. She has been by his side through all of this, helping to feed him and laying by his side."
It's been a particularly traumatic few months for Kim who, last month, was robbed at gunpoint by masked invaders who stormed her Paris apartment, tied her up, put her in the bath, and stole $10 million worth of jewellery.
Despite this, she has been visiting Kanye in hospital constantly and been his rock.
A source said: "She has been an unbelievably devoted spouse. He's a lucky man."
But her Paris ordeal may have affected Kanye as she wasn't able to attend as many of his tour dates as usual following the attack.
A source recently explained: "In the past, he snapped back quickly. This has been going on for years. In the past when Kanye seemed to struggle, no one took it too seriously. The attitude was more like it was just Kanye being Kanye.
"Things would go back to normal. This time is much different.
"Without having Kim by his side during the tour as planned, Kanye wasn't able to snap back. Kim being absent because of her own struggles seems to be why things are different with Kanye this time."