The group behind the proposals wants to open a one-form entry school for 25 pupils in September 2014 - but could still open this year if the Dfe signs off the plan and a suitable site can be found.
The application was produced in partnership with education provider, CfBT Schools Trust, which recently opened Oakbank Secondary School in Ryeish Green and All Saints Junior School in Reading.
The CfBT Schools Trust is a subsidiary of CfBT Education Trust, which is one of the world's largest educational charities and has more than 40 years experience.
Victoria Webb, a spokesman for the group, said there were two main reasons for the application.
She said: "There is a need for a local community-based primary school in the Evendons areas", and added it would create a "real choice for parents".
The school would hope to offer a diverse curriculum promoting the development of 21st century knowledge and skills, in particular in the areas of enterprise education and entrepreneurship.
It would also focus on STEM subjects - science, technology, engineering and mathematics.
The parent group is still searching for suitable sites within the area and reviewing their financial viability and logistics.
If any reader has any details of sites that might be suitable for a small primary school in or near to Evendons Lane, they should contact the group by email (firstname.lastname@example.org).
The group is preparing for its interview with the Department for Education which is expected to take place in late February/early March.