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 family’s 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 Archie’s 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The hospital has not confirmed when treatment will be withdrawn, but Christian Concern says the family have been told it will be withdrawn on Saturday.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 Court’s hospice ruling earlier on Friday, Archie’s 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 Archie’s best interests to be moved.
She said: “Archie’s 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 Archie’s family’s “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.”