Leeds City Council has previously identified the site that is currently occupied by Fearnville Leisure Centre as the best location for the development.
And now council chiefs have announced that a feasibility study has been commissioned that will deliver designs and costings for the proposed facility.
Plans to demolish the existing centre and build the new one in its place were drawn up following an initial public consultation process and an evaluation of other potential sites.
Opened in 1980, Fearnville was once among the city's best-used leisure centres but is now, by the council's own admission, in need of "vast modernisation".
Coun Mohammed Rafique, the council’s executive member with responsibility for sport, said: “I am pleased that, following a site appraisal and a public consultation, we are now at the stage to move forward with a feasibility study for a new leisure and wellbeing centre to be built on the same site as the existing Fearnville Leisure Centre.
“We want our leisure centres to be at the hub of our communities and offer facilities that are not only high-quality but importantly also affordable.
"A potential new leisure and wellbeing centre will certainly offer this for the people of east Leeds, and we look forward to bringing the results of the feasibility study back to the executive board for consideration, once this work is completed.”
Plans for major changes to sports provision in east Leeds have been in the pipeline for many years, with council bosses announcing as long ago as 2008 that they were considering closing Fearnville, which is off Oakwood Lane in Gipton.
More recently, proposals were unveiled – and subsequently dropped following major local opposition – for a new secondary school to be built on Fearnville Fields, which adjoin the leisure centre.