Evans' parents wanted the European Court of Human Rights to examine issues surrounding the case, but ECHR judges rejected their bid.
Mr Justice Hayden is scheduled to oversee another hearing in Alfie Evans' case in the Family Division of the High Court in Manchester at 3.30pm today, following reports that the gravely ill toddler, who has been granted Italian citizenship, was this morning still alive and breathing without a ventilator after having life support withdrawn last night.
He gave lawyers permission to release a recording of the hearing to the Press Association.
"They say Alfie's suffering".
She said she was not "completely satisfied" that Alfie had been granted Italian citizenship.
But Mr Justice Hayden dismissed Mr Diamond's application, saying it amounted to a "last-ditch appeal". The Italian government has made representations to the Foreign Secretary and applied for permission to intervene to save Alfie's life. It means that Alfie can not breathe, or eat, or drink without sophisticated medical treatment.
'I am not going to provide more time, ' he said.
A United Kingdom hospital is holding an Italian citizen hostage and intends to deprive him of life-giving treatment against the wishes of his parents. "I love Alfie and I love Kate, I will not give up".
Yesterday there were scenes of chaos outside the Liverpool hospital, as protesters tried to charge inside the building.
They ran towards the main doors but police blocked their way.
The case drew interventions from the pope and President Donald Trump, and became a flashpoint for debates on the rights of children and parents, the responsibilities of hospitals and the role of the state.
Doctors were unable to definitively diagnose the child's condition, but they believe he suffers from a rare degenerative neurological disorder which is ultimately fatal, causing him to suffer from seizures. Specialists say his brain has been "eroded".
Doctors in the United Kingdom have not been able to make a definitive diagnosis of the 23-month-old child's degenerative neurological condition, but they have said keeping him on life-support would be "futile". They had already lost one round of fights in the High Court, Court of Appeal, Supreme Court and the ECHR.
Alfie has survived much longer than the doctors predicted, lending support to the request from Alfie's parents for Alfie to be seen by medical experts in Italy.
Inside the hospital, Alfie's family confronted police officers who had set guard at Alfie's room to prevent anyone from removing him from the hospital.
The couple are now arguing that Alfie is being wrongly "detained" at Alder Hey and have made a habeas corpus application.
The Register has learned from a source close to the family that Justice Hayden "rejected every argument" and "completely disregarded everything and everyone".
On Friday Supreme Court justices said they would not intervene.