Connie Yates and Chris Gard had said they wanted 11-month-old Charlie to spend his final days with them at home.
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.
They say a hospice would be a better plan.
Lawyers representing the couple on Wednesday told a High Court judge overseeing the dispute about a change of heart.
They said the couple now wanted a move to a hospice.
But they said Charlie’s parents were still in dispute with doctors over the detail of care plans.
Mr Justice Francis began analysing the dispute at a hearing in the Family Division of the High Court and said he would make a decision if agreement could not be reached.
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.
Great Ormond Street bosses wanted Charlie to stay at a hospice for a shorter period.
Mr Armstrong said Great Ormond Street bosses were not satisfied that a properly qualified specialist would be in charge under the couple’s plan.
Mr Justice Francis asked journalists and members of the public to leave the court for a short period.
He said he wanted to give parties the chance to air thoughts privately.