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 said it is not practical to provide the level of life-support treatment to Charlie at the couple's home for days.
The issues include that his ventilator would not fit through their front door and so they said 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 said he will make a decision on Wednesday if agreement cannot be reached.
He said having heard the evidence, the chances of Charlie's parents' wishes being fulfilled were small. The hearing is due to resume at 2pm.
Charlie's parents became embroiled in the new fight with doctors a day after abandoning attempts to persuade the judge to let their son travel to America for experimental treatment.
Barrister Grant Armstrong, who leads the couple's legal team, suggested to Mr Justice Francis that hospital bosses were placing obstacles in Charlie's parents' way.
He said: "The parents wish for a few days of tranquillity outside of a hospital setting. The parents had hoped that Great Ormond Street would work with them.''
He said the couple felt there was a ''brutality'' in taking Charlie to a hospice.
Barrister Katie Gollop QC, who leads Great Ormond Street's legal team, said staff were not creating "obstacles".
She said nothing could be further from the truth - she said staff had "moved heaven and earth" for Charlie. But she said the couple's needs had to be balanced against Charlie's best interests.
She said Great Ormond Street staff had found an ''excellent hospice'' which would give Charlie and his parents the space, privacy and protection they needed.
