The council says the girl, who turned four in August, is too young to start school. However, the parents want their daughter to start in a reception class before Christmas.
The parents, who cannot be named for legal reasons, are said to be "deeply worried" about research which suggests summer-born children can be disadvantaged at school.
They believe their daughter will be better off starting school as soon as possible.
Their solicitor, Ian Wise, said they feared the girl would score lower in her first national curriculum tests at key stage 1 - three years away - if she only receives seven terms of education, as opposed to nine terms if she started school now.
Sheffield city council says the child cannot start primary school until the spring term. Initially, the council had insisted the girl could not start reception class until her fifth birthday next year.
However when a place became available last month, it offered to let her begin in April. The parents say that is illegal and out of step with the Government's early-years policy.
Mr Wise argues that under the Government's pledge to provide a free nursery place for every four-year-old who wanted one from last month, the parents have a right to a place in a reception class.
Last week the couple won the first round of their battle when the High Court gave them permission to sue the council.