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But 27-year-old Anderson has rejected the chance to move to St Andrews - opting instead to stay at Selhurst Park.
"It's a big disappointment," said Bluce. "We've worked extremely hard the last three or four weeks to try to get him here.
"The clubs had agreed everything and it was down to the player in the end but he refused."
Blues even tried to persuade Andersen to join on loan until the end of the season but it is understood that Anderson does not want to be uprooted from his London home.
Bruce said: "I'm sure he has his reasons, good luck to him. We will just have to press on and see who else is available."