Alfie Evans' parents are to challenge high court ruling that they cannot take the seriously ill toddler to Italy for treatment.
On Tuesday a high court judge said they could take him home from Alder Hey hospital, but not abroad.
A spokeswoman for the Christian Legal Centre, representing Alfie's parents, said their appeal is due to be heard at the Court of Appeal on Wednesday afternoon.
Mr Justice Hayden, speaking after an emergency hearing in the Family Division of the High Court in Manchester, called Alfie a "warrior", but said the case had reached its "final chapter".
He decided that Alfie's parents Tom Evans and Kate James could not have medical experts in Italy examine their son, as they had wished.
Instead, the judge asked Alder Hey Children's Hospital in Liverpool to consider permitting them to take their son home.
He advised the couple to "explore" other options, such as removing him from intensive care either to a ward, a hospice or his home.
The 23-month-old boy at the centre of a life support battle has a degenerative neurological condition and is considered to be in a semi-vegetative state.
A spokesman for Alder Hey said: "This evening the High Court again ruled that it is in Alfie's best interests to continue with the end of life care plan developed by the clinical team who have cared for him throughout.
"Our top priority therefore remains in ensuring Alfie receives the care he deserves to ensure his comfort, dignity and privacy are maintained throughout."
The judge rejected claims by his father that Alfie was "significantly better" than first thought, having survived unaided for 20 hours after doctors first withdrew life support on Monday night.
But Mr Justice Hayden said in his ruling: "With little, indeed no hesitation, I reject that. The brain cannot regenerate itself and there is virtually nothing of his brain left.
"There is, in truth, with great respect to the efforts of (parents' lawyer) Mr Diamond, no substance to this application, which represents, at least within the court process, the final chapter in the case of this extraordinary little boy."
Speaking to lawyers representing Alfie's parents and the hospital, the judge asked: "If there were a more constructive attitude from the family might other options become possible, away from Alder Hey?
"I'm not suggesting this, I don't want it to be taken as an indication from me. One of the things Tom Evans said, if it can't be Italy or Munich, which it cannot be, was whether they could take Alfie home."
But a doctor treating Alfie, who cannot be named for legal reasons and appeared in court in medical scrubs, said that would require a "sea change" in the attitude of Alfie's family.
The medic said the hospital feared that in the "worst case" Alfie's family would try to take the boy abroad.
The couple, who are from Liverpool, said doctors in Rome were willing to treat him. Italy granted the boy Italian citizenship, and the Pope has intervened in the case.
A spokeswoman for the Christian Legal Centre, which is assisting them, said an air ambulance was "waiting outside Alder Hey Hospital ready to take Alfie to hospital in Italy."
Earlier on Tuesday Mr Evans, speaking outside Alder Hey, said doctors were "gobsmacked" that his son was breathing nine hours after his life support ended.
"He's still breathing now," Mr Evans 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."
Alfie was born on 9 May 2016. He suffered seizures and was taken to hospital in December that year.
He is currently being hydrated and given oxygen to stop him becoming distressed.