In line with usual policy it has not commented on his condition.
Last week, the UK Supreme Court turned down the latest appeal by parents of 23-month-old Evans, who suffers from an undiagnosed degenerative neurological condition, to take their son to Italy for treatment.
The hospital, in Liverpool, has assured patients that the mood is "calm" despite a "police presence" outside, where supporters of Alfie are gathered.
The children's hospital also urged people not to contact its staff or switchboard seeking news about the youngster.More news: Jackson First Tiger Taken in NFL Draft After Guice Slips
The Strasbourg-based court said it received an application from the parents of 23-month-old Alfie Evans on Friday to potentially delay Alder Hey Children's Hospital in Liverpool from removing him from life support.
But the judge, Mr Justice Hayden, asked doctors if "other options" are possible to allow his family to take him home after life support was withdrawn.
Alfie Evans breathes unaided in his mother's arms after his life support was withdrawn.
A High Court judge dismissed fresh submissions heard in private from lawyers representing Alfie's parents via telephone link on Monday evening.
Medics say he has a degenerative neurological condition destroying his brain, and it is in his best interests to withdraw life support, but his parents want to take him overseas for treatment.More news: Princess Charlotte's floral dress sells out within 24 hours
"He is still working, he's doing as good as he can but we do need him to be supported in the next hour".
"Because he's been doing it for nine hours totally unexpected, the doctors are gobsmacked and I do believe he will need some form of life-support in the next couple of hours and I think he ought to be respected and given that".
Facebook / Alfie EvansAlfie Evans has a rare degenerative condition and doctors in the United Kingdom say further treatment would be "futile" and also cruel.
"A common sense approach must now be for Mr Justice Hayden to discharge all the court orders which detain Alfie and seek to end his life in Alder Hey, and give him the chance to be treated and looked after in Italy".
Pope Francis tweeted: "Moved by the prayers and huge solidarity shown little Alfie Evans, I renew my appeal that the suffering of his parents may be heard and that their desire to seek new forms of treatment may be granted". "He's not even on a ventilator and he's not suffering", he said.More news: Man left critically ill after clash between Liverpool and Roma fans
"They left him for six hours without food, water and oxygen", he said. "It's come to a point when his mum's actually asleep next to him so she can go to sleep, she feels comfortable with him", he said. It's not changing his breathing but it's oxygenating his body, ' he said.