The Trust is already bidding for the Athletes’ Village which will be turned into 2,800 apartments post 2012.
Its latest offer is a speculative bid for the freehold of the land including the main stadium, aquatics centre and media centre.
If the Olympic Park Legacy Company takes the bid seriously it could have to start a formal tender to allow rivals to bid for the whole site.
The Trust wants to turn the Games site into a science and technology park alongside a new residential community.
In a statement last night a spokeswoman said: “The Wellcome Trust has been shortlisted by the Olympic Delivery Authority to submit a proposal for the purchase and long term management of the residential properties known as the Athletes Village.
“In exploring this opportunity further, we are giving detailed consideration as to how we may also become investors in the wider Olympic Park and optimise the legacy of the Olympics.
“To this end we are currently meeting with a broad range of stakeholders to explore this opportunity.”