Parents at a Bristol school that wants to become an academy have accepted a proposal of support from an education foundation, the council has said.
The private St Ursula's School announced the academy plans earlier this year.
A council spokeswoman said an offer from Oasis Community Learning had been accepted.
The Catholic school, in Westbury-on-Trym, has struggled to attract new pupils.
It currently has fewer than 200 children.
If the bid is successful, St Ursula's would be the ninth academy in the city.
A final decision rests with the Department for Education.
Bristol North West MP Charlotte Leslie said there would be an announcement by the end of June.