The family of Archie Battersbee were "devastated" that all legal routes have been exhausted, campaign group Christian Concern has said.
The 12-year-old must spend his final days in hospital after the High Court ruled he could not move to a hospice.
The family requested the European Court of Human Rights (ECHR) intervene, but was told it "fell outside" its scope.
Archie has not regained consciousness since an accident at home in Southend, Essex, on 7 April.
The familys long legal battle to continue his life-sustaining treatment ended when the ECHR said it "would not interfere" with the UK courts rulings, paving the way for support to be stopped.
They hoped to move him to a hospice but doctors warned he was too unstable to move by ambulance and it would "hasten premature deterioration".
The High Court ruled Archie should remain at Royal London Hospital in Whitechapel, east London.
The family sought permission to appeal against the decision, but that bid was rejected by three justices at the Court of Appeal.
They then asked the ECHR to intervene, but late on Friday, the court said the request could not be dealt with.
A spokesman with campaign group Christian Concern, which is supporting Archies family, said: "All legal routes have been exhausted.
"The family are devastated and are spending precious time with Archie."
The hospital has not confirmed when treatment will be withdrawn, but Christian Concern says the family have been told it will be withdrawn on Saturday.
Responding to the High Courts hospice ruling earlier on Friday, Archies mum, Hollie Dance, said: "All our wishes as a family have been denied by the authorities.
"We are broken, but we are keeping going, because we love Archie and refuse to give up on him."
Archie was found unconscious at home and his mother believes he may have been taking part in an online challenge.
He suffered "catastrophic" brain injuries and doctors think it is "highly likely" he is brain-stem dead.
Life-sustaining support, including mechanical ventilation and drug treatments, has been in place since April.
In her ruling earlier on Friday, Mrs Justice Theis concluded it was not in Archies best interests to be moved.
She said: "Archies best interests must remain at the core of any conclusions reached by this court.
"When considering the wishes of the family, why those wishes are held, the facilities at the hospice, what Archie is likely to have wanted... the risks involved in a transfer... and the increasing fragility of his medical condition, I am satisfied... he should remain at the hospital when treatment is withdrawn."
Mrs Justice Theis also noted Archies familys "unconditional love and dedication", which she said had been a "golden thread that runs through this case".
"I hope now Archie can be afforded the opportunity for him to die in peaceful circumstances, with the family who meant so much to him as he clearly does to them."
Archie is found unconscious by his mother after an incident at their home in Essex. He is taken to Southend Hospital.
Archie is transferred to The Royal London Hospital in Whitechapel where he has been treated ever since.
The NHS trust that runs the Royal London starts High Court proceedings by asking for Archie to undergo brain stem testing.
Mrs Justice Arbuthnot rules that brain stem testing should be carried out.
Two specialists try to administer brain stem function tests, but they are unable to as Archie did not respond to a peripheral nerve stimulation test, a precursor to the brain stem test.
A hearing is held to decide if further MRI scans should be conducted. Archies parents did not consent on the basis that moving Archie could harm him.
The court approves further MRI scans, which are carried out on 31 May.
A final hearing is held to hear evidence on whether Archies life-support treatment should continue.
The High Court judge rules that Archie is "dead" based on MRI scan results and that treatment could be withdrawn.
The family ask the Court of Appeal to reconsider the case.
The Court of Appeal says that a new hearing to determine Archies best interests should take place.
A new hearing is held in the High Court with evidence given before Mr Justice Hayden.
Mr Justice Hayden rules that life-support treatment should end, saying continuing it is "futile".
Three Court of Appeal judges support the High Court ruling that treatment can end.
The Supreme Court rules out intervening in the case and supports the Court of Appeal ruling.
The family make an application to the United Nations.
A UN Committee writes to the UK government asking for a delay in withdrawing treatment while they consider the case.
The government asks for an urgent hearing to review the case.
The Court of Appeal refuses to postpone withdrawal of treatment until the UN can hear the case.
The Supreme Court refuse the familys application for permission to appeal the Court of Appeal ruling.
European Court of Human Rights refuses an application from the family to postpone the withdrawal of Archie’s life support.
Archies parents make a legal application to move their son to a hospice for end of life care.
A High Court judge rules that Archie cannot be moved to a hospice for withdrawal of treatment.