Lawyers say the baby could become the first person born in England or Wales who will not legally have a mother.
The baby is the child of a single parent who was born a woman but now lives as a man after undergoing surgery.
Judges have heard that the man had been biologically able to get pregnant and give birth but had legally become male by the time the child was born.
He wants to be identified as the child's “father” or “parent” on a birth certificate but a registrar has told him that the law requires people who give birth to be registered as mothers.
Sir Andrew McFarlane, president of the family division of the High Court, is due to decide whether only either “father” or “parent” can be listed on the child's birth certificate following a trial scheduled to take place at the High Court in London in February.
The man has taken legal action after complaining of discrimination.
He says forcing him to register as the child's “mother” breaches his human right to respect for privacy and family life.
The case has been analysed at High Court hearings in London in recent months and lawyers representing the man are lined up against lawyers representing the Registrar General for England and Wales and government ministers.
It hit the headlines in June after another judge oversaw a preliminary hearing.
Mr Justice Francis said then that the issue had never been raised in a court in England and Wales before.
The judge said if the man won his fight ministers might have to consider changing the law.
He said the baby could not be identified in media reports and said journalists should not reveal the baby's gender or age, or the man's age, and should not give any clue as to where the man and the child lived.
Lawyers say other transgender men have given birth but have been registered on birth certificates as mothers.
They say if the man wins his fight the child will be the first person born in England or Wales not to legally have a mother.
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