On Sunday, the Vatican also released a statement saying that the Pope was following the case of the sick child, "with affection and sadness" and was close to his parents: "For this he prays that their wish to accompany and treat their child until the end isn't neglected".
A European court has ruled that the life support machine can be turned off for Charlie Gard, an infant born with a rare mitochondrial depletion syndrome.
Connie Yates and her husband Chris Gard filed a case in the European Court of Human Rights that ruled June 27 the boy could not be taken to the USA and should be removed from life support.
The London hospital where Charlie Gard is living his last days has refused a transfer request from Bambino Gesu pediatric hospital in Rome for legal reasons.
The hospital has offered to keep Charlie on life support and allow his parents to decide "how to handle" ending his life, including when to switch off life support, it said.
US President Donald Trump has also offered to help and on Tuesday the Sun reported an unnamed US hospital was ready to treat him free of charge despite United Kingdom and European court's rulings against useless treatment.
A White House statement said: "Upon learning of baby Charlie Gard's situation, President Trump has offered to help the family in this heartbreaking situation".
The unnamed hospital has allegedly offered a new experimental treatment at no cost - if he is granted permission to travel.
She said that she has asked the hospital's Health Director to contact London's Great Ormond Street Hospital, where Charlie is being treated, to verify if the baby can be transferred to the Vatican-owned facility.
Columnist Katie Hopkins tweeted Tuesday: "Charlie Gard's life should be in his parents' hands". But three courts, including the Supreme Court of England, have chose to detach Charlie from the vital life support, to give him "a dignified death", "in his own interest".
The Great Ormond Street Hospital where he is staying has argued the child would suffer harm because there is no prospect he will recover.
The case has resurfaced a decades-old debate over euthanasia and the use of life support, issues that have been fought in most corners of the world and that have often seen medical and religious arguments collide.
The specialist, who can not be named for legal reasons, said therapy would provide a "small chance" of a meaningful improvement in Charlie's brain function. And that battle officially ended this past week when the highest court in Europe, the European Court of Human Rights, decided in favor of the hospital.
They state that Twitter does not censor tweets. "He is praying for them, in the hope that their desire to accompany and care for their own child until the end will be respected".