It has asked designers to create plans for an outdoor athletics facility, an aquatic centre for regional competitions and training facilities for athletes and the local community.
Arup has already worked up concept designs for a replacement ( pictured).
But those behind the scheme will need to convince planners that the contribution to the community from these new facilities would outweigh the loss of destroying a 1963 listed building.
Under current legislation, the demolition of a listed building can occasionally be justified under these circumstances.
However, Julian Harrap Architects is working with the Twentieth Century Society (C20) to design an alternative scheme to preserve the centre and its surroundings, which it plans to reveal in the next two months.
C20 caseworker Cordula Zeidler said: 'We're not happy that (the LDA) is looking for a replacement.
'We don't think they've looked at the possibilities of reusing the existing, structurally sound centre properly.'
The local community has rallied behind the idea of bulldozing the centre. The vast majority of those consulted by the LDA have backed demolition and the creation of a state-of-the-art facility.
The LDA claimed that this level of support, which stood at 77 per cent in a survey, will help to see this new scheme completed by 2010, two years before the 2012 Olympics.
London Assembly member for Lambeth and Southwark Valerie Shawcross said: 'For too long, Crystal Palace Park has been under used, with areas that feel run down or unsafe.
'I am especially pleased to see the strength of support for a new sports centre.'
Interested practices have until mid-March to respond to an OJEU notice advertising the project.