Both competitions are for conceptual planning and design schemes, including stadiums, landscaped parks and accommodation.
The Olympic park includes an 80,000-seat stadium, an 18,000-seat gymnasium, a 15,000-seat swimming centre, accommodation for athletes and extensive conference and exhibition facilities.
The Wukesong site includes an 18,000-seat basketball stadium and temporary fields for baseball and softball.
One source claimed HOK Sport would be one of the favourites to pick up the job because of its experience. The architect has designed stadiums in Nanjing, Hong Kong and Taipei, Taiwan, and carried out planning work for the 2000 Sydney Olympics.
The firm also acted as a consultant on Beijing's 2008 Olympic bid.
Final submissions for both competitions are due on 2 July. First prize for the Olympic park competition is £175,000; first prize for the other contest is £56,000.
The winners will be announced at the end of July.
China is expected to spend £16.5bn preparing Beijing for the games: £1.2bn on building the stadiums and £15.3bn on infrastructure and environmental work.
Foreign trade experts believe UK firms will win several infrastructure and support services contracts. The British Consultants Bureau is leading a construction and engineering trade mission to China next month to prepare the ground for bids for Olympic-related contracts.
Deputy prime minister John Prescott is visiting Beijing at the same time.
The BCB said several construction firms, consulting engineers, architects and lawyers had expressed an interest in going.