Local and national lawmakers want to establish an anchor tenant quickly for the venue causing most headache for organisers to avoid the 537 million pound stadium becoming a white elephant after the Olympics as has been the case with some previous Games.
Football, rugby and cricket clubs have been mentioned but they have been put off by the organisers' commitment to retain an athletics track around the pitch.
The latest parties expressing an interest were the new owners of Premier League club West Ham United.
The Olympic Park Legacy Company (OPLC), a public sector company set up to manage planning and development of the Olympic Park in legacy, has invited organisations interested in operating in, or locating to the stadium after the Games, to come forward with expressions of interest.
The soft market testing will be completed by the middle of June, and could be followed by a public procurement exercise.
Its future will be settled by the end of March next year.
"A successful stadium legacy is vital to the company's long-term aspirations for the Olympic Park," said Andrew Altman, OPLC chief executive.
Use of the stadium could include sporting, community, education, visitor attraction and commercial interests.
The cost of the stadium has doubled from its initial estimate, but it is potentially one of the most important venues for attracting jobs and investment to the Olympic Park in a previously run-down part of east London.
Uncertainty over its future was undermining overall legacy planning, some lawmakers have said.
Stadium plans deliberately included flexibility in its construction and its 80,000-seating capacity is due to be reduced to 25,000 after the Games to host international athletics events.
But more seating could be needed if it was to be turned into a football stadium, especially after organisers of England's 2018 World Cup bid included it on their list of potential venues.
