A Vatican pediatric hospital says experimental therapy "could have been an opportunity" to help Charlie Gard, but it was too late to start care for the critically ill baby.
Mr Gard and Ms Yates, who are aged in their 30s and come from Bedfont, west London, had asked Mr Justice Francis to rule that Charlie should be allowed to undergo a therapy trial in NY.
"Unless by 12pm tomorrow the parents and guardian and Great Ormond Street hospital can agree alternative arrangement, Charlie will be transferred to a hospice and extubated shortly thereafter", he said.
In April, Justice Francis ruled that the hospital could allow the child to die after doctors and the court had deemed treatment futile, against the wishes of the child's parents.
After hours of legal argument, the parents accepted the only options were GOSH or a hospice. "The parents had hoped that Great Ormond Street would work with them".
He said on Wednesday that the time had come for a decision to be made. "May I pay tribute to those nurses for volunteering", he said.
Barrister Grant Armstrong, who leads Charlie's parents' legal team, indicated that the couple wanted to privately fund treatment at a hospice where Charlie would stay for a number of days before life-support treatment was ended.
Mr Justice Francis ordered that, unless there was agreement by midday today, Charlie would be moved to a hospice at some point soon and have his ventilation tube taken out thereafter.
Once there, the baby's life support eventually would be switched off.
Doctors at Great Ormond Street opposed that, saying it would not help and could cause Charlie more suffering.
The U.S. physician who sought to provide an experimental treatment to 11-month-old Charlie Gard denied having any financial interest in the therapy Wednesday, according to The Telegraph.
The London hospital insists the family must find six nurses and three specialist doctors to care for him if they want to manage his final days.
He said he wanted to give parties the chance to air thoughts privately.
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.
Following the hearing, Charlie's godfather James Evers accused GOSH of putting "arduous conditions" in the way of Ms Yates and Mr Gard's wishes.
The hospital disagrees. It says Charlie had suffered irreversible brain damage by January as a result of a series of seizures, and his responsiveness has not changed since then.