They say they want a few days of “tranquillity” outside the hospital.
He requires invasive ventilation to breathe and can not see, hear or swallow.
Connie Yates and Chris Gard and their son’s doctors now agree he should die in a hospice but can not find common ground on the length of time he will have there.
On Monday the High Court decided there was no treatment option left for the child.
Ms Yates and Mr Gard had initially said they wanted 11-month-old Charlie to spend days with them at home before dying.
After Mr Armstrong asked for 48 more hours to find an intensivist [board-certified physician who provides special care for critically ill patients] who can take care of Charlie, the judge said the indecision between the two groups is “compounding” the parents’ misery.
Mr Justice Francis ruled that unless the parents and GOSH came to an agreement by noon today, Charlie will be taken to a hospice and life support treatment will end soon after.
An alternative arrangement appears unlikely, given the total breakdown in relations between the parents and the hospital.
On a Facebook page set up for Charlie, the couple posted on Wednesday: “URGENT we need a pediatric intensive care consultant to come forward to assist and facilitate with a hospice stay by 12pm tomorrow, we will pay privately”.
“What if it was your child”, Connie Yates shouted at the hearing before storming out in tears. “I hope you are happy with yourselves”.
The care plan for Charlie must honour his parents wishes about the time and place of his passing, but also be safe, spare Charlie all pain and protect his dignity, the hospital said in a statement issued on Tuesday.
However, it later emerged that he was a GP with “no experience of intensive care”, according to Victoria Butler-Cole, the lawyer for the guardian.
Butler-Cole said the parents should spend the last few days of Charlie’s life with him, not with their lawyers.
Questions remain about whether Charlie could have benefited from the experimental treatment, had it not been delayed for months during the legal battle between Charlie’s parents and the hospital. Their lawyer accuses Great Ormond Street Hospital of putting obstacles in their way.
The couple had fought all the way to the European Court of Human Rights for permission to have their son treated, but were refused by judges at each step. It has suggested that he should be removed from life support within hours of being transferred to a hospice.