The parents of Alfie Evans are appealing against a High Court decision preventing the seriously ill boy from being taken abroad for treatment, lawyers have confirmed.
A spokeswoman for the Christian Legal Centre, representing Alfie's parents, said the case is due to be heard at the Court of Appeal on Wednesday afternoon.
On Tuesday a judge ruled the boy may be allowed home from Alder Hey Children's Hospital, but will not be allowed to go to Rome for further treatment.
The 23-month-old confounded doctors' expectations when he continued to live after life-support was withdrawn on Monday night, his father, Tom Evans, said.
"The court of appeal have reached out to us and said they are going to set back three judges to hear the case," Mr Evans told reporters outside hospital on Tuesday night.
"In reality, he could be in Italy right now. We all know the military air force are ready to take him and a team of doctors are there.
"We've also got a German air ambulance team, who attempted to take him in the first place, ready... the reality is these people are eager to get him out of the country and I'm not giving up because Alfie's breathing away, he's not suffering."
Mr Evans revealed that Alfie had at times needed to be helped with his breathing, telling reporters: "At some point I had to give him mouth-to-mouth because his lips went blue and he was really fighting with his breathing so me and his mum were giving him mouth-to-mouth."
At an earlier High Court hearing in Manchester, Mr Justice Hayden described Alfie as "courageous" and a "warrior", but said the case had now reached its "final chapter".
He rejected claims by Mr Evans that his son was "significantly better" than first thought because he had been breathing unaided for 20 hours after doctors first withdrew life support.
Instead, the judge said the best Alfie's parents could hope for was to "explore" the options of removing him from intensive care either to a ward, a hospice or his home.
But a doctor treating Alfie, who cannot be named for legal reasons, said that for Alfie to be allowed home would require a "sea change" in attitude from the child's family, and they feared that in the "worst case" they would try to take the boy abroad.
Mr Justice Hayden ruled out the family's wishes to take the child to the Bambino Gesu hospital in Rome, following interventions from the Pope and the Italian authorities.