Lawyers representing Charlie Gard's parents and Great Ormond Street Hospital are due to return to the High Court in the next few hours.
Chris Gard and Connie Yates on Monday abandoned attempts to persuade a judge to allow their terminally-ill 11-month-old son to travel to America for experimental therapy.
But the judge who has analysed litigation is scheduled to oversee a further hearing in the case at 2pm in the Family Division of the High Court in London on Tuesday.
A case listing gives no clue about issues Mr Justice Francis might be asked to consider.
On Monday, the couple said they wanted to "spend our last precious moments" with Charlie.
Ms Yates said she did not expect her son to live until his first birthday on August 4.
Bosses at Great Ormond Street Hospital have not said when Charlie's life-support equipment will be turned off.
But in late June, when litigation appeared to have come to an end after European Court judges refused to intervene in the case, a hospital spokeswoman said there would be ''careful planning and discussion'' before life-support treatment ended.
Mr Gard and Ms Yates, who are in their 30s and from Bedfont, west London, had asked Mr Justice Francis to rule that Charlie should be allowed to undergo a therapy trial in New York.
Doctors at Great Ormond Street said the therapy would not help and that life-support treatment should stop.
Mr Justice Francis in April ruled in favour of Great Ormond Street and said Charlie should be allowed to die with dignity.
Charlie's parents subsequently failed to overturn his ruling in the High Court, Court of Appeal and Supreme Court in London.
They also failed to persuade European Court of Human Rights judges to intervene.
But the couple recently returned to court, saying they had new evidence, and asked Mr Justice Francis to change his mind.
The couple abandoned their legal fight on Monday after concluding that Charlie had deteriorated to the ''point of no return''.
Ms Gard read a statement during a hearing in the Family Division of the High Court.
''We are now going to spend our last precious moments with our son Charlie, who unfortunately won't make his first birthday in just under two weeks' time,'' she said.
''Mummy and Daddy love you so much, Charlie, we always have and we always will and we are so sorry that we couldn't save you.
''Sweet dreams, baby.
''Sleep tight, our beautiful little boy.''