Judge hears proposals as he decides where Charlie Gard will end his life
Connie Yates and Chris Gard want their 11-month-old son to spend his last days with them at home before dying.
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.
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Hide AdThey say a better plan would be for Charlie to move to a hospice.
Mr Justice Francis analysed the dispute at a hearing in the Family Division of the High Court on Tuesday and says he will make a decision on Wednesday if agreement cannot be reached.
Barrister Grant Armstrong, who leads Charlie's parents' legal team, indicated that a doctor with intensive care experience had been found.
He told Mr Justice Francis that Great Ormond Street nurses had volunteered to help.
Mr Armstrong said the plan was for the doctor to have discussions with Great Ormond Street staff shortly.