The European Court of Humans Rights (ECHR) has rejected a last-ditch appeal by the family of Archie Battersbee.
The court said that it would "not interfere with the decisions of the national courts to allow the withdrawal of life sustaining treatment from Archie Battersbee to proceed".
The Christian Legal Centre (CLC), which is supporting the family, said they are considering their options after receiving offers from doctors in Japan and Italy to continue treatment.
Responding to the news, Archie's mum, Hollie Dance, said: "This is another heartbreaking development in our fight for Archie's right to live. We have been contacted by doctors in Japan and Italy who say they are willing to treat Archie. Why can't we give him a chance?
"The NHS, the government and the courts in this country and Europe may have given up on treating him, but we have not.
"The whole system has been stacked against us. Reform must now come through Charlie's Law so that no parents have to go through this.
"In a worst-case scenario, we want to take Archie to a hospice, but the hospital have said that we cannot do that despite previous promises. We have been told all along that this is all about Archie dying with 'dignity', and yet we are told we cannot take him to a hospice where it is quiet and we can spend time with him as a family without the chaos at the hospital.
"We will fight to end for Archie's right to live."
The family made an urgent application to the ECHR after the government and Supreme Court said that requests to keep Archie on life support from the UN Committee on the Rights of Persons with Disabilities (UN CRPD) were not legally binding.
On Thursday, the family filed another last-ditch application, this time to the High Court asking for permission to move Archie to a hospice and for him to be allowed palliative oxygen when attempting breathe.
Andrea Williams, chief executive of the Christian Legal Centre, said: "This is a story about a mother's love. She was catapulted into a whirlwind of legal battles and media attention all because she believed in giving her beloved son more time.
"Even though the whole system has come against her she has stood with her legal team against all the odds.
"The hospital and courts say this is all about Archie's dignity which means he should die quickly and at a specified time. The parents don't agree that it is dignified and in his best interests to die. Even the parents' request to move him to a hospice is being denied as undignified.
"Common humanity requires a different way of doing this. We continue to stand with the family as they consider their next options."