The majority of local residents would like to the see the 1963 Grade II*-listed recreation centre redeveloped, according to the London Development Agency (LDA).
More than 3,500 people have had their say on the LDA's proposals for major improvements to Crystal Palace Park - that includes the current National Sports Centre - with many ideas gaining as much as 90 per cent support.
However, some ideas were not so popular. Four options for a controversial site known as the 'Norwood Triangle' have been ignored by the public, with none of the options gaining either overwhelming support or opposition.
Two of those options included apartments on the corner of the park, which would help to fund either an underground car park for the town centre or other improvements.
Valerie Shawcross, London Assembly member for Lambeth and Southwark, said: 'It is fantastic to see so many people grabbing the opportunity to have their say on the future of this important park - and of course to see the strength of support for major improvements.'
The consultation will continue until 20 December.