After it was announced in May that locals would like to see the LCC-designed landmark demolished, the LDA is now meeting with stakeholders to see how it could take such a possibility forward, according to the Twentieth Century Society (C20).
But before it could act on such an option the LDA would have to solve a quandary - how to reconcile the needs of the public with the fact that the building is Grade II* listed and as such cannot be legally torn down.
According to C20 caseworker Cordula Zeidler, the LDA is attempting to use planning policy guideline PPG15 to justify the centre's destruction.
This would involve resolving that demolition would meet public requirements for a new sports centre as opposed to getting the facility de-listed and then razing it to the ground.
An LDA spokesman confirmed that recent meetings had been taking place between the relevant stakeholders. This has come after a period of discussions with the public that kicked off with a formal consultation last September.
The Crystal Palace Park Main Working Group, which draws its members from the ranks of interested community members, has since agreed that there is large-scale public support for a new sports centre. It believes that this should have modern facilities and be closer to public transport.
The group also thinks that the site of the current sports centre should, as much as possible, be returned to parkland.
In response to these wishes, LDA executive director Tony Winterbottom said: 'This is a clear message from local people about what they would like in the park.
'Now we need to establish what to do with the current centre - which is a listed building - as well as what funding is available for a new centre.
'If we can raise the right levels of investment and funding, the park and sports facilities could undergo major rejuvenation to once again become a major destination for the capital.'
The LDA became involved in Crystal Palace Park when the 2012 Olympic bid helped to focus attention on existing sports infrastructure in the capital. The LDA will take on responsibility for the sports centre next February and has an option to take on the park as a whole by 2009.
It will make proposals for the park and sports centre in a planning framework later this year, when there will be another public consultation.