A couple have mounted a challenge after a High Court judge ruled that their ''profoundly neurologically disabled'' two-year-old son could be moved to a palliative care regime.
Mrs Justice Parker said the youngster's life should not be artificially prolonged and gave medics permission to provide only palliative care.
But the boy's parents have asked the Court of Appeal to consider the case.
Their solicitor, Kavi Mayor, who is based at Jung & Co Solicitors, says a Court of Appeal hearing is likely to take place in London soon.
He said the boy would not be moved to a palliative regime until an appeal judge had made a decision.
Officials at Guy's and St Thomas' NHS Foundation Trust, who have responsibility for the boy's care, had asked Mrs Justice Parker to make a decision.
She delivered a ruling in May after analysing evidence at a hearing in the Family Division of the High Court in London.
The boy's parents said they were devastated, and said Mrs Justice Parker's ruling "effectively condemns their son to death".
They said specialists had "not explored all possible options".
A trust spokesman said staff had acted in the boy's best interests and said medics would "continue to provide the best possible care".
Specialists said the boy suffered from an incurable but unidentified neurological disorder and said his condition was deteriorating.
Nurses said he had stopped smiling and that he grimaced but no longer giggled when tickled.
Doctors said ''further invasive interventions'' would be distressing and burdensome for the little boy and would have little or no therapeutic benefit.
The youngster's parents disagreed with the idea of providing only palliative care and implementing an ''end-of-life plan''.
They said all treatment options should continue to be available.
Mrs Justice Parker had concluded that it was not in the boy's best interests to "artificially prolong" his life.
The judge said the boy could not be identified.