Midrar Ali, who will be three months old on Wednesday, has a significant brain injury which doctors say he will never recover from and it would be kinder to allow him to die.
But his father, Karwan Ali, 35, and mother, Shokhan Ali, 28, have launched a legal bid for more time to treat their son.
Their case came before the Family Division of the High Court, sitting in Preston, on Tuesday for a preliminary hearing.
His mother had a normal pregnancy but complications during birth meant her baby's brain was starved of oxygen.
Neil Davy, representing Manchester University NHS Foundation Trust, told Mr Justice MacDonald that experts had carried out a series of tests on Midrar's brain stem and the hospital's main priority is that the child's "dignity is maintained".
Mr Ali told the court that he had changed solicitors and was awaiting a decision on whether he will receive legal aid before he can be represented.
He said: "It's important the court know that Midrar is not in any pain, or suffering or deteriorating. In fact, Midrar has grown, he's got some sensitivity, he's opening his eyes a little bit.
"So I don't understand the rush of the hospital to do the procedure."
Mr Justice MacDonald ruled that a further hearing should take place, with a date yet to be fixed, before a final hearing on January 20 to decide on the baby's future treatment.
He told the parents: "All these things you have just told me will be considered by the judge."
He rejected an application for reporting restrictions on the case made by the hospital trust on Tuesday.
A further reporting restriction application by the trust will be made in the coming days, the hearing was told.
Outside court , Mr Ali, a biomedical scientist, said the hospital had tried to "convince" him and his wife to end life support due to their son's brain stem death.
But he added: "No doctor, no biologist can keep a dead person alive for three months. The body does not work without the brain. I'm a biologist, I know that. The body does not work without the brain. We have evidence of him responding.
"The question is 'What's the rush?'"
The Alis' plight echoes that of similar recent cases including Alfie Evans, from Liverpool, born with an undiagnosed neurodegenerative disorder, who died last year, and Charlie Gard, whose parents fought a similar battle in 2017.