The baby will be transferred and taken off of life support unless the hospital and parents reach an agreement by noon local time tomorrow.
Connie Yates and Chris Gard fought a long battle against the Great Ormond Street Hospital in London, drawing worldwide attention, to bring their son to the USA for experimental treatment.
But doctors caring for Charlie at Great Ormond Street Hospital in London say it is not practical to provide life-support treatment to Charlie at the couple's home for days.
Mr Gard and Ms Yates, who are in their 30s and come from Bedfont, west London, had originally asked Mr Justice Francis to rule that Charlie should be allowed to undergo a therapy trial in NY.
On Wednesday, the lawyer said Gard and Yates had accepted the need to transfer Charlie to a hospice but differences remained over how that should happen.
The hospital said it had found an "excellent hospice" with the space and privacy, and the facilities needed.
The judge is also considering placing Charlie in a hospice for his final days.
Charlie Gard has a rare genetic disorder and brain damage.
Nicholas Francis, the High Court judge who has presided over an agonizing series of hearings on the case, had given the parents until yesterday to find a team of intensive-care specialists willing to oversee Charlie's care at home.
The judge said he envisaged Thursday's proceedings being "the final hearing", in a case which has been going through the courts for five months.
It said: "Please only email if you can help us!" If an agreement can not be reached, Charlie will be taken to a hospice where they will remove him from life-support. The hospital recommended a hospice, but said that life support would be withdrawn after a few hours, contrary to Chris and Connie's wishes of wanting days with their son.
Charlie's parents abandoned their fight to allow him to be flown to the USA for experimental treatment on Monday, having determined it was no longer viable because of muscular atrophy he had suffered while the case went through the courts.
"We have decided it's no longer in Charlie's interest to have treatment". On July 17, Charlie was examined by USA neurologist who claimed that an experimental therapy could provide up to a 10 percent chance of improvement in the child's condition.
His parents said they knew the chance of the experimental treatment working was slim, but they wanted to try anyway for Charlie's sake.
The parents gave up the legal battle on Monday, saying the latest scans showed Charlie's condition had deteriorated to the point that no recovery was possible.