The 12-year-old’s life support is due to be withdrawn on Wednesday morning.
Archie Battersbee’s parents said they will submit an application to the European Court of Human Rights (ECHR) in a bid to postpone the withdrawal of his life support.
Life-sustaining treatment for the 12-year-old has been in place since April and is set to be withdrawn later.
An appeal against the decision to end treatment was refused by the Supreme Court on Tuesday.
Mum Hollie Dance said the latest court bid needed to be made by 09:00 BST.
She said: “Our solicitors will be filing to the European Court of Human Rights. They’ve been given a strict timeline of 09:00. Again, no time whatsoever.
“Every single court case we’ve had we’ve had no time at all, one or two days to prepare and get the whole case together.”
Archie was found unconscious at home in Southend-on-Sea, Essex, on 7 April.
He has never regained consciousness and his mother believes he may have been taking part in an online challenge when he suffered brain damage.
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