Councillor Paul Haslam believes the views of parents and the local community will have a "big sway" in the future of the school which last week requested a closure consultation after being rated as inadequate and placed into special measures.
The rating from Ofsted inspectors in January 2020 meant the school must become a sponsored academy, but it failed to find a backer.
Merger talks with Grove Road Community Primary School also failed when the nearby school pulled out of the proposals.
Conservative councillor Haslam - who represents the Bilton area and has been a governor at Woodfield for four years - said: "Just because there is a consultation to consider closing, it doesn't necessarily mean the school will close.
"It does mean there are difficulties and nobody is hiding from that fact.
"It will be a very important consultation when it gets started and I will be very keen for lots of people - not just parents - to get involved."
Woodfield has fallen into financial difficulties ever since a big drop in pupil numbers in 2018. At the time, the school had 155 pupils, but this has now dwindled to 37 with 11 pupils due to leave in July.
And because pupil numbers determine the level of funding that a school receives, Woodfield has forecast to be in a deficit of £329,800 by 2023/24.
The school has also had six different headteachers over the last four years.
Councillor Haslam said he was "devastated" that the school has found itself in this situation, but added he believes it could have a future if there is demand for pupil places.
He said: "I believe Woodfield should have a school - it is an area of deprivation and we all know the best way of deprivation is good education.
"What I want to see at Woodfield is a high-calibre school that the people deserve.
"The leadership has developed a great curriculum and really set the school on its way. If we were able to get back to 70 or 80 pupils, that would show progress and we would be able to work out of this.
"But on the pupil numbers that we currently have, that is not going to work."
A statement from North Yorkshire County Council last week said it would communicate directly with parents "in the coming days on the many questions they will have."
The authority's director of children and young people's services, Stuart Carlton, said: “The county council hoped that the proposed amalgamation would provide a solution to retain education on the school site, but that was not to be.
“I would like to thank the leadership and governors of Woodfield Community Primary School for their diligence in exploring the issues and I share their sadness that closure must now be considered.
“We will now move at pace to seek approval to consult on a proposal that the school should close during the next academic year."
By Jacob Webster, Local Democracy Reporter