A High Court judge could decide next week whether terminally-ill baby Charlie Gard should be allowed to travel to the United States for treatment.
Mr Justice Francis is scheduled to analyse the latest expert evidence at a hearing in the Family Division of the High Court in London on Monday and Tuesday.
The judge examined issues at a preliminary hearing on Friday and said he would need to know whether there was "new material" which could make a "difference".
Lawyers representing Great Ormond Street Hospital in London, where 11-month-old Charlie is being cared for, said they had "yet to see" any new evidence.
Chris Gard and Connie Yates want Mr Justice Francis to rule that their 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 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 change his mind.
Earlier this week the American specialist - Michio Hirano, a professor of neurology at Columbia University Medical Centre in New York – travelled to London to examine Charlie for the first time and discuss the case with Great Ormond Street doctors.
Lawyers say they will examine reports from that gathering – and data from new scans carried out on Charlie - over the weekend.
Mr Justice Francis has told Charlie's parents that he will not re-run the case but will consider any "new material".
Barrister Grant Armstrong, who represents Charlie's parents, told the judge on Friday that a "range of opinions" had been expressed when experts gathered at Great Ormond Street.
But barrister Katie Gollop QC, who is leading Great Ormond Street's legal team, said: "We don't yet have any of this apparent new evidence."
Lawyers said Dr Hirano and Charlie's parents could give evidence at next week's hearing.