The family are seeking legal permission to move the 12-year-old from the Royal London Hospital to a hospice. The application is currently being considered by the High Court. Archie’s mother said she wanted to say goodbye to her son “in a peaceful hospice”.
However, doctors have warned there is “significant risk” in moving him.
Archie, who suffered traumatic brain injuries in April, has been relying on life-sustaining support such as mechanical ventilation and drug treatments continuously ever since.
A High Court hearing took place on Thursday to consider the application.
No changes will be made to Archie’s care until a ruling has been made public, it is understood.
The latest application comes after the European Court of Human Rights (ECHR) refused a request from the family to delay the withdrawal of Archie’s treatment.
His treatment was due to be withdrawn on Wednesday but was delayed while the ECHR considered the appeal.
But the ECHR ruled it “would not interfere” with the UK courts’ rulings.
In a statement, Archie’s mother, Hollie Dance, said the latest appeal to move her son to a hospice was about his “dignity”.
She said: “I pray that the High Court will do the right thing.
“If they refuse permission for us to take him to a hospice and for him to receive palliative oxygen it will simply be inhumane and nothing about Archie’s ‘dignity’.
“We will fight to the end for Archie’s right to live.”
She said she wants her son to be in a “peaceful hospice to say goodbye and spend time with his family, uninterrupted by the noise and chaos”.
A July High Court order requires that Archie remains at the Royal London Hospital while treatment is withdrawn.
Lawyers acting on behalf of Barts Health NHS Trust, which runs the Royal London Hospital, said it would oppose any application to transfer Archie to a hospice on “both a procedural basis and best interests basis”.
The letter from the legal team continued: “The trust 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.”
It said the trust believes the family are now “at the end of the procedural options open to them”, adding: “Any further delay is not in Archie’s best interests.”