The Prime Minister's comments came after US president Donald Trump and the Pope tweeted their support for the boy, who has been at the centre of a lengthy legal battle involving his parents and doctors at Great Ormond Street Hospital (GOSH).
Mrs May told MPs: "It is an unimaginable position for anybody to be in and I fully understand and appreciate that any parent in these circumstances will want to do everything possible and explore every option for their seriously ill child.
"But I also know that no doctor ever wants to be placed in the terrible position where they have to make such heartbreaking decisions."
The parents of Charlie, Chris Gard and Connie Yates, lost a legal battle to take the 10-month old to the US for experimental treatment.
Mrs May said: "I am confident that Great Ormond Street Hospital have and always will consider any offers or new information that has come forward with consideration of the wellbeing of a desperately ill child".
At Prime Minister's Questions, the family's MP Seema Malhotra said it was "clear that if Charlie remains in the UK there is no further treatment available and that life support will be switched off".
The Feltham and Heston MP urged Mrs May to do "all she can" if there was the possibility of Charlie being flown to the US for treatment.
Labour MP Ms Malhotra said: "If there is any room for discretion within the court rulings for Great Ormond Street to allow Charlie to leave and to transfer his care to doctors at Columbia University, and he is sufficiently stable to receive treatment, will the Prime Minister do all she can to bring the appropriate people together to try to make this happen?"
Mrs May said: "I'm sure the thoughts of all Members of the House are with the family and Charlie at this exceptionally difficult time."
The Prime Minister's comments came after the Vatican's paediatric hospital stepped in to offer care after Pope Francis called for Charlie's parents to be allowed to "accompany and treat their child until the end".
But renowned scientist and genetics expert Lord Winston criticised attempts to transfer the 10-month-old from the central London specialist children's hospital.
"I think, first of all, one has to accept the loss of a child is about the worst injury that any person can have and, secondly, I think the autonomy of parents is probably sacrosanct because a child can't give approval, can't give consent," he told ITV's Good Morning Britain.
"But having said that, these interferences from the Vatican and from Donald Trump seem to me to be extremely unhelpful and very cruel, actually, because this child has been dealt with 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."
Successive legal attempts by Charlie's parents failed as judges in the High Court, Court of Appeal and Supreme Court in London ruled in favour of GOSH doctors, while the European Court of Human Rights declined to hear the couple's appeal.
Charlie's parents, both aged in their 30s and from Bedfont, west London, are now spending the last days of their son's life with him, after being given more time before his life support is turned off.
Charlie suffers from a rare genetic condition and has brain damage.
The High Court considered evidence from a specialist who would oversee any treatment Charlie had at a hospital in the US.
The specialist, who cannot be named for legal reasons, said therapy would provide a "small chance" of a meaningful improvement in Charlie's brain function.
Charlie's plight has touched people around the world and the family have received donations totalling more than £1.3 million to take him to the US for therapy.
Mr Trump said: "If we can help little #CharlieGard, as per our friends in the U.K. and the Pope, we would be delighted to do so."