Preece joined the Cumbrians last Friday after being sacked as player-manager by Bury as part of cost-cutting measures.
Carlisle claim that Bury would only release Preece's registration if Carlisle player-boss Paul Simpson agreed not to pick him for Friday's game.
In order to sign Preece in time for last weekend's game against Torquay - in which the 36-year-old opened the scoring - Simpson reluctantly accepted the conditions of the agreement.
But Carlisle claim they had little option but to agree, and that Bury had no right to demand such a clause in the contract as Preece was a free agent.
"Paul has been on the phone to Bury to try and sort it out, but at the moment it looks like Andy won't be playing on Boxing Day," said a Carlisle spokesman.
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