“People in High Green are very excited about it.”
Alternative locations would involve either building at Mortomley Park, also in High Green, or replacing Stocksbridge Leisure Centre.
Sheffield Council officials favour High Green as the most suitable location because it is close to a large area of population.
Stocksbridge is viewed as more difficult for people from surrounding areas to access.
Negotiations about the new centre have been taking place for the last few months involving Sheffield Council, Ecclesfield Parish Council, Chapeltown Leisure, the not-for-profit community organisation running Chapeltown Baths, the NHS and Sport England.
The facility is to be built as part of Sheffield’s £10 million Centre for Sport and Exercise Medicine project, which will also see improvements to Graves Leisure Centre, Norton, and Concord Leisure Centre, Shiregreen.
Ecclesfield Parish Council has been asked to divert funding currently paid each year towards the running of Chapeltown pool for the new facility.
Sheffield Council also wants the parish council to give it the baths site, which would be sold to help raise extra funding.
Officials stress the money available for the new centre is not Sheffield Council funding so would not have been available to save Don Valley Stadium or keep open the existing Stocksbridge Leisure Centre.
Sheffield Council, Ecclesfield Parish Council and Chapeltown Leisure declined to comment, and Penistone and Stocksbridge Labour MP Angela Smith was unavailable for comment.
Sheffield Centre for Sports and Exercise Medicine is one of three being developed around the country as part of the Government’s Olympic Legacy commitment.
The other centres will be in Loughborough and London.
A spokesman for Deputy Prime Minister and Sheffield Hallam MP Nick Clegg said: “Hosting the Olympics was a once-in-a-lifetime opportunity for Britain and it provided a great opportunity for the NHS too.
“The centres will share research findings and best practice with the entire NHS so the whole country benefits.
“This is a great opportunity for Sheffield.”