News of the possible visit emerged as Charlie’s parents mounted the latest round of a legal battle at a hearing in the Family Division of the High Court in London.
Chris Gard and Connie Yates have asked a judge to rule that 11-month-old Charlie, who suffers from a rare genetic condition and has brain damage, be allowed to undergo a therapy trial in the United States.
However, specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, say the therapy is experimental and will not help him.
They say his life-support treatment should stop.
The couple, who are in their 30s and come from Bedfont, west London, have already lost battles in the High Court, Court of Appeal and Supreme Court in London. They have also failed to persuade European Court of Human Rights judges to intervene.
The couple say there is new evidence and want Mr Justice Francis to carry out a fresh analysis of their case.
In April, the judge ruled in favour of Great Ormond Street and said Charlie should be allowed to die with dignity.
Mr Justice Francis began considering their claims at a hearing in the Family Division of the High Court in London yesterday. The hearing is due to resume today.
The doctor gave evidence to the hearing yesterday via a video link from the US. Mr Justice Francis has ruled that the doctor cannot be identified.
The judge said he wanted to hear what the doctor thought had changed since the judge gave his ruling in April.
The doctor said he had clinical data which was not available in April. He said he still thought the therapy was “worth trying”.
The doctor estimated there could be a 10 per cent chance of improvement in muscle strength and a “small but significant” improvement in brain function.
He said he had not seen or examined Charlie.
The judge said it may be a good idea if the doctor travelled to London to see Charlie and meet Great Ormond Street specialists.
Lawyers told the judge that the doctor might be able to visit in the next few days.
Barrister Grant Armstrong, who is leading Charlie’s parents’ legal team, said the couple thought they had fresh evidence.
“The parents seek to re-open the case in relation to the chances of success of treatment,” he said.
Mr Armstrong told the judge: “The material shifts the balance of best interests clearly in favour of continuation of life and in favour of treatment.”
Mr Justice Francis said he was unlikely to give any ruling today.