Galliard said it proposed to regenerate the area and build a high-rise urban village and low-income housing.
London architect BUJ is heading the design team, which includes Hong Kong architect Joanlin Au.
The government is to decide next week whether to accept property developer Legacy's £125m bid.
Prime minister Tony Blair is backing Legacy but after reports that the bid had hit difficulties and might collapse, other rival bids have re-emerged.
Japanese bank Nomura is reportedly preparing a joint bid with the Duke of Westminster and Pierre-Yves Gerbeau, the dome's former chief executive, to buy the troubled site.
Nomura had been the government's preferred bidder before pulling out of an agreement last September, citing insufficient disclosure of the dome's financial state.
Stanhope chief Sir Stuart Lipton told Building website's Live News that his firm may support Legacy's bid.