Parents hoping to set up the school have submitted their application to the Department of Education and hope 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.
Cllr Charlotte Haitham-Taylor said: "I have met and been impressed by the drive and the passion of parents who I know are working hard to establish a free school in Evendons ward.
"Whilst our primary strategy will ensure we deliver sufficient school places, this initiative will help improve parent choice and as such it is welcomed. I wish parents every success in their application to the secretary of state".
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 parents group hope the school would create a "real choice for parents".
It would hope to offer a curriculum promoting 21st century knowledge and skills and would 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 (email@example.com).
The group is preparing for its interview with the Department for Education which is expected to take place in late February/early March.