Charlie Gard's parents are preparing for the latest stage of their legal fight over treatment for the terminally ill baby.
A judge is listed to further analyse issues at a hearing in the Family Division of the High Court in London on Friday.
Chris Gard and Connie Yates want Mr Justice Francis to rule that their 11-month-old son, who suffers from a rare genetic condition and has brain damage, should be allowed to undergo a therapy trial overseen by a specialist in New York.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, say the therapy is experimental and will not help.
They say life support treatment should stop.
Charlie's parents, who are in their 30s and come from Bedfont, west London, have already lost battles in the High Court, Court of Appeal and Supreme Court in London.
They have also failed to persuade European Court of Human Rights judges to intervene.
But the couple say there is new evidence and want Mr Justice Francis, who in April ruled in favour of Great Ormond Street and said Charlie should be allowed to die with dignity, to carry out a fresh analysis of their case.
Mr Justice Francis has considered the couple's new claims at preliminary hearings.
Last week, he suggested that the American specialist - Michio Hirano, a professor of neurology at the Columbia University Medical Centre in New York - should travel to London to meet Great Ormond Street doctors and other clinicians.
Dr Hirano examined Charlie and discussed his case while visiting Great Ormond Street on Monday and Tuesday.
Court listings indicated that Friday's hearing would last less than two hours.
Lawyers representing Great Ormond Street and Charlie's parents are expected to update the judge on discussions held at the hospital.