The hospital was scheduled to take the child off of life support last month after his parents lost an appeal to take him to the U.S. for experimental treatment.
But Britain's courts have refused permission on the grounds it would prolong his suffering without a realistic prospect of it helping the 11-month-old child.
Charlie will be examined early this week, in London, by Dr. Michio Hirano, a neurologist at New York's Columbia University Medical Center.
A British consultant has criticised the "magic potion" treatment being offered by an American doctor who is flying to the United Kingdom tomorrow to examine Charlie Gard.
But Dr Hirano, 55, believes his experimental theory could give Charlie "11% to 56% chance of clinically meaningful improvement".
Hirano, who testified via video-link on Thursday, said it was worth trying treatment that has recently emerged.
Charlie suffers from the rare genetic condition, which causes progressive muscle weakness and brain damage.
Hirano is one of the pioneers of nucleoside - an experimental therapy which is being sought by Charlie's parents, Chris Gard and Connie Yates.
The High Court has previously ruled that Charlie's life support should be removed to enable him to die with dignity.
The couple has already lost battles in the High Court, Court of Appeal and Supreme Court in London, and they have failed to persuade the European Court of Human Rights to intervene in their case.
It is not clear if Hirano or the other doctor have performed the experimental therapy on other mitochondrial DNA depletion syndrome patients, however, it is known that he is an expert on this particular syndrome and has published several research articles on the subject, most of which, however, involve animal models.
The Vatican said Pope Francis was following the case with "affection and emotion" and "expresses his own closeness to his [Charlie's] parents".
Specialists at Great Ormond Street Hospital have fought the parents' bid for treatment because they don't think it will help and may cause him pain.