Archie Battersbee's life support will be withdrawn at 11am, unless his family launch a High Court bid by 9am to move him to a hospice.
His parents plan to file the application by the deadline.
They lost their latest legal appeal to stop doctors ending life-sustaining hospital treatment for their brain-damaged son after a European court said it "will not interfere" with the decisions of UK courts.
The 12-year-old's family had applied to the European Court of Human Rights (ECHR) to intervene as they fought to postpone treatment being switched off.
But the Strasbourg-based court said it would not interfere with previous rulings by "national courts".
Archie is being kept alive by a combination of medical interventions, including ventilation and drug treatments.
Now Barts Health NHS Trust in London has said the treatment will end at 11am on Thursday unless the family apply to the High Court by 9am to move him to a hospice.
It insisted: "Any application will be opposed on both a procedural basis and best interests basis."
The trust said it "continues to put Archie's welfare and best interests at the forefront of its decision making about his care. It believes that Archie's condition is unstable and that transferring him even a short distance involves significant risk".
But if an application is made, then treatment will continue while the bid is heard, it said.
The family have made it clear they want him moved to a hospice, so he can receive palliative care.
Speaking earlier, Archie's mother Hollie Dance said: "We've now got to fight to see if we can get him out of here to have a dignified passing at a hospice.
"It's just unfair. The fact is as a parent we've got no rights for our children, it's disgusting."
A spokeswoman for the family said: "We think it is completely barbaric and absolutely disgusting that we're not even allowed to choose where Archie takes his last moments.
"Hospices are well and truly designed for palliative and respite care. Archie is now obviously on palliative care, so there is no reason whatsoever for him not to take his last moments at a hospice.
"The hospice has said that they will take him."
The child has been in a coma since he was found unconscious by his mother at home in Southend, Essex, in April.
Judges have heard Ms Dance discovered her son with a ligature over his head, after she believes he took part in an online challenge.
Doctors treating Archie at the Royal London Hospital in Whitechapel, east London, believe he is brain-stem dead and say continued life support is not in his best interests.
But his family have insisted the treatment should continue, saying the youngster's heart was still beating, and he had gripped his mother's hand.
Speaking about the setback in the European court, Ms Dance said it was "another heart-breaking development" and she was feeling "absolutely deflated, and so let down… obviously that was our last option".
On Tuesday, she and Archie's father Paul Battersbee lost a bid in the Supreme Court - the UK's highest court - to keep the treatment going.
A day earlier, the Court of Appeal refused a bid by the UN's Committee on the Rights of Persons With Disabilities to delay the withdrawal of treatment until it had the chance to review the case.