A number of options are on the table for it and the two other council-run leisure centres in Dudley and Stourbridge.
The review is due to the “very challenging” financial situation the council is facing, according to urban development director John Millar.
He said: "The council is currently considering a range of options with regard to the future management of the borough's leisure centres to ensure that residents and visitors alike have affordable access to leisure facilities, which in turn contributes to the health and wellbeing of those using them.
"The council does face a very challenging financial situation and all council service areas have been challenged to find savings whilst maintaining service provision wherever possible."
He added: "No decisions have been made at this time and we are continuing look at what options are available."
Councillor Patrick Harley, leader of Dudley's Conservative group, said he expected the council to have an idea of the direction it would take by next month.
He added: "All options should be on the table, whether that is straight forward reorganisation, taking the radical step of handing over to a private consortium or a not-for-profit organisation or we set up an arm’s length company and still retain a stake in running."