The other firms competing are FaulknerBrowns, Ward McHugh Associates and Arup.
Project developer Lee Valley Park Authority is set to announce the winner next week.
Doubts have been raised about funding for the project, which will host the 2005 World Athletics Championships. So far, the client, UK Athletics, has secured only £72m in funding.
A spokesperson for Lee Valley Park Authority said the developer and client were confident of raising the extra £23m required.
The project is set to start on site next December.