The firms in the hunt are Balfour Beatty, BAM Nuttall, Carillion, Lend Lease, Skanska and VolkerFitzpatrick.
The firms have already fought off competition from 145 contractors who registered their interest in February.
The work has been spit into packages for the North Park and South Park contracts and winners will be announced in December.
Work will involve preparing the park for future development including the removal of temporary venues and structures, removal of Games-time elements of permanent venues and the reconfiguration of roads, bridges and other infrastructure.
Mark Reynolds, Deputy CEO of Mace, said: “We are thrilled to be one of the few companies to have been involved with the regeneration of the Olympic Park from inception, with the original master-planning and contributing to the Candidate City bid, through delivery of London 2012 Olympic and Paralypmic Games with CLM Delivery Partner (the ODA’s delivery partner) and now onto delivering the legacy.
“We look forward to developing a world-class legacy with the Olympic Park Legacy Company.”