Doctors have agreed to give Charlie's parents, Chris Gard and Connie Yates, from west London, a few more days to spend with their son before his life support is switched off.
A British hospital that plans to disconnect terminally ill infant Charlie Gard from life support has rejected treatment help from the Vatican's children's hospital. Trump has not spoken directly to the family, Aguirre Ferre said, but administration officials have reached out via the British government.
Their talks are likely to be dominated by the North Korea missile crisis and a post-Brexit trade deal, but Number 10 was said to be compiling a detailed briefing on Charlie's case in anticipation of questions from Mr Trump.
Pope Francis had expressed hope that the parents' desire to "to accompany and care for their own child to the end" will be respected.
That was because Charlie was being treated "at a hospital which has huge expertise in mitochondrial disease and is being offered a break in a hospital that has never published anything on this disease, as far as I'm aware".
President Donald Trump offered to help a terminally ill British baby on Monday, saying on Twitter that "if we can help little #CharlieGard, as per our friends in the United Kingdom and the Pope, we would be delighted to do so".
Charlie suffers from a rare genetic condition which causes brain damage and muscle depletion and no one can be certain whether or not he feels pain, GOSH has said.
On Tuesday, the parents lost a bid to take Charlie to the USA for trial therapy when the European Court of Human Rights sided with earlier rulings that continued treatment would cause "significant harm" and that life support should end.
So you can either - depending on your view of President Trump - you can either see this as the President weighing in to help a very sick child and his parents, or a president who's using a very sick child and his parents as political props to appear as though he's actually helping, when in reality it would take extraordinary intervention on behalf of the President to go in the face of multiple high courts here in Britain and the European Court of Human Rights.
After Pope Francis and President Donald Trump spoke out in support of Charlie, the Vatican's Bambino Gesu Children's Hospital asked whether the child could be transferred to Rome to receive care.
Charlie's mother said: "The support from the Pope and the President has given us hope".
They said they felt "let down" by the legal decision. "The president is just trying to be helpful if at all possible", she said, calling the situation "heartbreaking".
"They believe in our case and understand why we believe it is right to continue fighting so hard to save Charlie".