Mrs Shephard is ready to allow the grant-maintained school in Gravesend to open the 40-place unit although the council has more than 800 nursery places in the area.
She has told Kent that she is minded to approve the proposal put forward by Holy Trinity GM primary. Forcing a local authority to fund non-statutory nursery places at an opted-out school would have major implications.
Kent claims that switching Pounds 45,000 from its budget to fund the Holy Trinity nursery class would be a "substantial misapplication of limited public funds". There are already two LEA units less than 400 metres away and a further 11, including a workplace nursery at a GM school, within a two-mile radius.
Early this year the Government signalled its willingness to allow GM schools to open nursery classes, but only in areas where the local authority had no formal objections. The Department for Education has had difficulties extending nurseries in GM schools for although the Funding Agency for Schools has paid for building work, running costs have come out of LEA budgets.
Local authorities might therefore legally challenge any decision to force them to fund nursery classes and Mrs Shephard's move has been opposed by all political parties in Kent County Council, which is now controlled by Labour and the Liberal-Democrats.
In a letter to the DFE the council says: "The clear, transparent and objective county policy is to locate further provision in areas of greatest social and economic need and where provision is limited."
The school has claimed that if had remained under local authority control its nursery proposal would have been accepted.
Three months ago, Robin Squire, the education junior minister, said if a GM school was able to show an LEA was expanding its nursery sector and that it could have expected to have a share in that programme if it had remained under council control, consideration would be given to funding the project.
In a formal response to the LEA's objections the school said it already had 56 names on a waiting list for the nursery and that it believed that the cost would be Pounds 35,000 and not Pounds 45,000.
The school said: "We believe that the objections are discriminatory because our school has GM status. If Kent County Council was truly committed to the greater development of nursery education it would realise that Holy Trinity's proposals were a cost effective and readily available means of expanding this provision."
* A new therapy centre for children under five with hearing and speech problems opens in London on September 12, writes Linda Blackburne.
Christopher Place, the Speech, Language and Hearing Centre, is intended to help parents such as Nigel and Judith Roberts who were devastated when their second child, like their first, was born profoundly deaf. There was no explanation and no family history of deafness.
Angela Harding, the centre's director who is also a teacher and therapist, believes it is the only centre of its kind in the UK.
About one child in 25 has delayed speech and there are 40,000 profoundly deaf babies in the UK.
Angela Harding said: "These early years are critical in the child's development. With the combination of an early diagnosis and skilled therapy parents can often see dramatic and positive results."