The BBC may handle the job itself, or hand it over to property partner Land Securities Trillium.
Construction managers are concerned that if the BBC hands control to Land Securities Trillium, Bovis Lend Lease will be favourite to win the contract because of its close relationship with Trillium at the White City site in west London.
One construction manager said: "There is a danger that the same thing that happened at White City could happen at Broadcasting House."
A source on the design team said the BBC could choose a different route for the Broadcasting House redevelopment. He said: "The BBC may want a more competitive process, to make it more open. That means whoever gets in as a construction manager would be in a good position for future work."
Land Securities Trillium took over the BBC's London property portfolio in September. The contract included the construction of a £200m studio complex next to the BBC's White City home.