RMJM was unable to comment on the scheme.
However, it is understood that all three firms were then ordered to reapply after pressure from the Australian government, which had been lobbying for Cox.
The project sources have indicated that this second contest, which was held in December, was also won by RMJM.
The winning team, which will be made public when official confirmation of its appointment is released, will be part of a consortium headed by a Chinese regeneration agency, the Beijing North Star Group.
RMJM first won the bid last September, beating off competition from two top international firms including Rem Koolhaas
The group is understood to have met on 15 January to debate the decision.
The building will be a centrepiece of the city-wide regeneration being undertaken for the 2008 Olympics, but could be used for other purposes.
A source close to the project said that the convention would be a big part of the games but could also be used for economic and political summits such as a meeting of the International Monetary Fund or a World Bank conference.
RMJM has experience of delivering large political projects. As well as the Scottish parliament, in March last year it completed the 8400 m2 Dubai International Convention Centre.