A consultation is to take place on the future of Chillerton and Rookley Primary School, in Chillerton.
It follows a formal request from the Stenbury Federation, which runs it.
There are 34 pupil numbers at Chillerton and Rookley Primary, which has room for 91.
The school received no first preference applications for the 2021/22 academic year.
It also has an estimated budget deficit of around £101,000 for 2020/21, forecast to grow to £225,000 by 2023 due to a decline in pupil numbers.
In a letter to the Isle of Wight Council, governors said amalgamating Chillerton and Rookley Primary School with its sister school at Godshill would "reduce the risk of both schools having to close due to budget constraints and falling pupil numbers."
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It insists it would ensure "high-quality education" for pupils.
County Hall has now launched a six-week, non-statutory public consultation.
Di Barker, chair of governors, said: ‘Governors are committed to ensuring all children in the Stenbury Federation have access to high-quality education by sustaining and building on recent improvements through effective and strategic use of our hardworking staff and existing resources.
"We have therefore written to the council to ask that they take steps to consider the future of Chillerton and Rookley Primary School."
Mark Snow, executive headteacher of the Stenbury Federation, added: "Staff and pupils have worked tirelessly to support me to improve both schools and I am immensely proud of the progress and effort we have made in some very challenging circumstances."
Councillor Paul Brading, Cabinet member for children's services, education and skills, said: "The governors have not reached this decision lightly but with the best interests of their children at heart.
"During the past few years, the Stenbury Federation has been through a period of leadership instability, deficit budgets and a requires improvement rating from Ofsted.
"However, since 2018, they have worked closely with the council to establish strong and consistent leadership, resulting in the rapid improvement of outcomes for their children.
"Now they believe a more sustainable educational offer should be considered and have therefore asked the council to start an initial consultation on the future of the school which we are happy to facilitate."
- To lodge your thoughts with the council's consultation, email your comments by March 19 to SandLBusinessSupport@IOW.gov.uk
- Tell the County Press what you think? Email a Letter to the Editor to editor@iwcp.co.uk
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