Specialists treating the youngster says she should stop receiving life-support treatment and move to a palliative care regime.
Her parents disagree.
Bosses at an NHS hospital trust responsible for the girl’s care have asked a High Court judge to decide what moves are in her best interests.
Mr Justice Williams is due to begin overseeing a trial in the in the Family Division of the High Court in London on Thursday.
Two other judges, Mr Justice MacDonald and Mrs Justice Lieven, have overseen recent preliminary hearings.
Judges have ruled that neither the girl nor the NHS trust, which is based in the north of England, can be named in media reports.
A barrister leading the trust’s legal team has told Mr Justice MacDonald that the youngster had a “severe and progressive life-limiting neuro-degenerative disorder” and “end-stage respiratory failure”.
Claire Watson said the girl’s condition was “terminal”.
Doctors thought that the girl, who could not “communicate verbally”, was in “discomfort”, she said.
She said the girl could not “communicate verbally”.
Trust bosses want a judge to rule that life-support treatment can stop.
The girl’s parents are opposing the trust’s application.
They say the youngster communicates with them with her eyes.
Barrister Sophia Roper, who is representing the couple, said relations between parents and specialists had “irretrievably broken down”.
The case has echoes of three other high-profile disputes involving four other children - Charlie Gard, Alfie Evans, Isaiah Haastrup and Tafida Raqeeb.
Judges ruled that doctors should stop treating Charlie, Alfie and Isaiah - and all three youngsters have now died.
A judge has yet to decide whether doctors should stop treating five-year-old Tafida.
Mr Justice MacDonald finished overseeing a trial on Friday and is expected to deliver a ruling soon.
Isaiah’s father, Lanre Haastrup, attended Tafida’s trial to show support for her parents, Shelina Begum and father Mohammed Raqeeb.