The Ridings school, Halifax, may become an academy after being judged "inadequate" by Government inspectors.
The West Yorkshire school was temporarily closed and branded a failure in 1996 when its headteacher resigned and staff threatened to strike over 60 "unteachable" children.
It was led out of special measures and appeared to have turned the corner, but Ofsted raised fresh doubts over standards after an inspection last October, just three months after the resignation of headteacher Anna White.
At a meeting of Calderdale council on Tuesday, it was agreed that talks would start over the possibility of replacing the school with an academy, or allowing a nearby secondary to take it over.
A private school has announced that it would abolish fees and join the state sector as an academy.
The pound;7,472-a-year William Hulme's grammar, Manchester, is the first member of the Headmasters' and Headmistresses' Conference to opt into the state sector.
The school, along with its junior department, will become an academy for children aged three to 18 from September.