Davina has lost a quarter of its first-week audience while The Apprentice has gained.
Only 3.5 million viewers watched Davina McCall's new chat show last week, but this has now fallen to 2.7 million. This was despite a guest line-up including Pierce Brosnan and Patrick Kielty.
BBC Two's The Apprentice, meanwhile, attracted 3.6 million viewers - almost double the first series opener's total. Last year's final was watched by 3.8 million.
"We are delighted with the success of The Apprentice, which has picked up where the last series left off in terms of ratings," a BBC spokeswoman said. "As for Davina, the audience is down on the first week but we are pleased with the show. We are giving it time to grow."