Making Notre Dame High School in Glasgow co-educational is being supported by the ruling SNP group on Glasgow City Council.
The future of the school is due to be discussed at a council meeting on 28 November.
As the SNP does not have a majority the outcome will depend on how other parties vote.
"We have yet to see the educational benefit for the change."
The school, founded in 1897 in the city’s west end , is a Roman Catholic establishment, but admits pupils of all faiths and those who have none.
"We hope the final barrier to local education is removed."
However, the ND4ALL campaign group said it was delighted.
A spokesman said: “We very much welcome this approach.
“We hope the final barrier to local education is removed, to have a fully inclusive school, inclusive of all children.
“We believe this will mean a brighter future for our children, community and co-educational Notre Dame High.”