The family have now lost multiple legal cases in the high court, the court of appeal, the supreme court and had their case rejected by the European court of human rights.
He has been in a "semi-vegetative state" for greater than a 12 months and is presently exclusively receiving oxygen after being taken off life assist final night time.
Tom Evans has refused to stop fighting for his boy, telling the media, "Alfie's still fighting, so I'm still fighting".
Last week judges at the Supreme Court, the highest court in the United Kingdom, rejected the family legal team's request for permission to appeal a court order to turn off the seriously-ill youngster's life support.
One of the clinicians at Alder Hey hospital said that moving Alfie can not take place for a few days at the earliest and that the hostility that they are facing from protesters - some of whom tried to storm the hospital on Monday - promises to make moving him hard.
The hospital argued that keeping Evans on a ventilator was "not in his best interests", and treatment was "futile" as well as "unkind and inhumane".
The medic said the hospital feared that in the "worst case" Alfie's family would try to take the boy overseas. The family lawyer said the toddler is doing "significantly better" than expected. "No matter what happens he has already proved these doctors wrong". Diamond, the family's barrister, said the case had reached "the highest levels of the Italian government" and that the Italian ambassador's chief of staff was in court for the hearing.
Police are having to block protestors from storming the hospital. News reports indicated the crowds had blocked roads and even tried to enter the hospital before police pushed the people back out.
On April 18, the pope met with Tom Evans, who is Catholic, in Rome.
The family have vowed to fight on for their son's cause. After the meeting, Pope Francis called for prayers for the toddler and said it is "our duty to do everything to preserve life".
"With little, indeed no hesitation, I reject that". The flight was reportedly prepared to depart within minutes of a ruling allowing Evans to leave.
"I've been following poor Alfie's story for a while and I wanted to show we're supporting him in Sheffield and hope he gets the treatment he needs", added the 50-year-old former carer.
The Associated Press reported earlier today that the Vatican had offered to provide Alfie with medical care. At that point, and as a result of the hospital's court action, the parents were stripped of their right to be decision-makers for their beloved child. But it was Horace, centuries later, who left us with a social principle particularly relevant in Alfie's case: "Laws without morals are dead". One might understand if a state-controlled health care system decided that further treatment would take valuable resources from patients who would benefit more, but that's not what is happening with Alfie.
In a similar case last July, British baby Charlie Gard died of a genetic disease after the courts blocked the baby's parents from transporting him to Italy.