Mr Justice Francis is scheduled to analyse the most recent expert evidence on at a trial starting in the Family Division of the High Court on Monday (July 24).
Chris Gard and Connie Yates want the judge to rule that their terminally-ill baby, 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 11-month-old Charlie is being cared for, say the therapy is experimental and will not help. They say life support treatment should stop.
Earlier this week, 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.
During his visit, he discussed Charlie's case with Great Ormond Street doctors.
On Saturday (July 22) and Sunday (July 24) lawyers will examine specialists reports, and data from fresh scans , ahead of Monday's hearing.
The judge considered preliminary issues at a hearing on Friday (July 21).
Barrister Katie Gollop QC, who leads Great Ormond Street's legal team, told the judge a report on a new scan made for "sad reading".
Charlie's parents reacted furiously to the news, saying they had not read the report.
Ms Yates burst into tears and Mr Gard yelled "evil" .
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 to change his mind , after he ruled in favour of Great Ormond Street in April, and said Charlie should be allowed to die with dignity.
Keep up to date with the latest news in west London via the free getwestlondon app.
You can set up your app to see all the latest news and events from your area, plus receive push notifications for breaking news.