The King Alfred Leisure Centre on Hove seafront may be sold as one of a number of options to be considered by Brighton and Hove City Council.
A project board will consider the future of the building and adjoining land. It will be chaired by Councillor Geoffrey Bowden.
Council leader Jason Kitcat said that a separate review was also looking at what sports facilities should be provided in Brighton and Hove and where.
Answering a question from Valerie Paynter, of the Save Hove campaign group, the Green councillor said that the project board would also look how much housing would go on the site.
She had asked whether the council might consider part-funding any proposal to prevent the need for 400-plus flats being built on the site to help pay for any new leisure centre there.
He said that cost sharing was a possibility, adding: “The project board will be happy to look at all outcomes.
“We’ve been approached by a number of developers so we know there’s interest in the site.
“Councillor Geoffrey Bowden will be chairing a project board with a view to preparing a tender.”
He said that anyone with costed proposals was welcome to approach the project board.
The Draft City Plan currently includes an allocation of more than 400 flats on the site to help pay for the building of a new leisure centre there.
A planning brief will also be prepared to spell out in more detail what the council expects from developers.
The council wants the school to use the site currently occupied by the Portslade Aldridge Community Academy sixth form.
Last week Hove businessman Rob Starr spelt out his plans for an arts and leisure complex on the King Alfred site under the working title The Lyrics.