Barbican Venture, the project's developers, have prepared revised proposals, following the results of the initial consultation in March.
A further consultation will be held throughout July so that residents can decide whether they would prefer a county standard swimming pool, releasing a capital receipt of £3m, or a community pool, providing an additional £1.4m, which would be used to fund refurbishment work at Yearsley and Edmund Wilson pools.
Revised details of the development plans for both options will be on display at the Barbican Centre on Wednesday, 16 July between 9.00am and 5.00pm, and on Tuesday, 22 July between 4.00pm ant 8.00pm.
Leisure chiefs are asking residents to have their say by collecting and returning a consultation leaflet from the Barbican, York Central Library or the Yortime Resource Centre; completing the on-line version available at www.york.gov.uk; or e mailing their responses to yortime@york.gov.uk
Anyone who provided a written response to the previous consultation will automatically receive a questionnaire, as will swimming groups and other interested partners.
Charlie Croft, the council's assistant director, lifelong learning and leisure, said: "This additional consultation will enable us to find out whether residents and users of the city's pools would prefer to have a county standard swimming facility at the Barbican, or community facilities, with additional funding to help refurbish the other pools."