Bambino Gesu' Hospital chief Mariella Enoc said their researchers had put their treatment protocol for Charlie Gard at the disposal of Great Ormond Street Hospital and the London hospital was "thinking of trying to verify it".
Charlie was born in August with mitochondrial DNA depletion syndrome, a progressive disease that causes muscle weakness and loss of motor skills, leaving those who have it unable to stand, walk, eat, talk and eventually breathe.
Charlie Gard, the terminally ill baby suffering from a rare mitochondrial disease, is at the centre of a legal tussle.
Dr Hirano has said he believes there is now a better chance the treatment would produce a meaningful improvement than there was when he gave evidence three months earlier.
The hospital gave Hirano, a doctor and professor at Columbia University Medical Center, an honorary contract, which gives him the same status as its own physicians.
The new High Court hearing was requested after the Vatican's children's hospital and the United States hospital said a new experimental protocol might work for Charlie, whose parents have been trying to secure a move to the US.
Charlie's parents, Chris Gard and Connie Yates, have raised £1.3 million (US$ 1.7 million) to take the baby to the USA for nucleoside therapy.
A judge ruled that Charlie's mother Connie Yates could be present for the gathering.More news: Yamana Gold's (AUY) "Market Perform" Rating Reaffirmed at Raymond James Financial, Inc
Great Ormond Street Hospital requested a new hearing after the New York-based neurologist claimed his treatment could now have a better chance of working.
The parents have previously lost battles against the hospital in the High Court, Court of Appeal and Supreme Court in London over Charlie's treatment.
It has prompted a fierce debate around the world about medical ethics and whether the hospital treating the child or his parents should determine his fate.
But last week, the case returned to the High Court after the hospital asked for a new hearing to consider new evidence from Hirano.
They have also failed to persuade European Court of Human Rights judges to intervene.
Specialists at Great Ormond Street say that the therapy is experimental and will not help Charlie.
Connie and Charlie's dad Chris, of Bedfont, West London, want a judge to rule the 11-month-old can have experimental treatment in the US.