Alfie Evans' parents want judges at the European Court of Human Rights (ECHR) in Strasbourg, France, to intervene after running out of legal options in the UK.
Tom Evans and Kate James, who are in their 20s and from Liverpool, have made an application to the ECHR after losing fights in the High Court, Court of Appeal and Supreme Court.
A High Court judge ruled that doctors at Alder Hey Children's Hospital in Liverpool could stop treating Alfie, against the wishes of his parents.
That decision was upheld by Court of Appeal judges and Supreme Court justices.
An ECHR spokesman said on Monday that lawyers representing Alfie's parents had written asking judges to "stay" the withdrawal of treatment, as an "interim measure", and to analyse arguments.
He said judges were considering the couple's requests and no decisions had been made.