The successful design and build contractor must come up with a design for football matches, 74,000 capacity athletics events and a 90,000 capacity revenue for concerts.
The contract could include retractable seating, depending on the cost and design.
Legacy Stadium Project, a joint venture between West Ham and Newham Borough Council, will handle procurement of the £100m transformation.
Works include the extension or replacement of the existing stadium roof to cover the majority of seating, building hospitality boxes and toilets. The project brief also includes offices and a new community athletics warm up track.
Legacy Stadium Partnership expects to let the contract in August to allow plenty of time to work up designs before transformation work starts in time for the May 2014 completion deadline.
Sir Robert McAlpine is a clear early favourite to take the job after successfully completing the original London 2012 Olympic stadium ahead of budget.
Firms have been given until 12 May to prequalify. Further details can be obtained by calling Ian Tompkins on 0771 119 4390 at Legacy Stadium Partnership or email Stadium.Transformation@trowers.com