Rangers are seven points adrift of safety after 15 matches and are still searching for their first win of the campaign, despite spending heavily during the summer.
The decision to shelve plans for the traditional end-of-year party was made by the players, Press Association Sport understands.
When asked about the decision, a club spokesman said "Have you seen the league table?"
New manager Redknapp, who replaced the sacked Mark Hughes last month, oversees his third match in charge at Wigan on Saturday.
Work Christmas parties are a long-standing tradition in Britain and football is no different.
Clubs have held lower-profile parties in recent years so as to avoid drink-related trouble and tabloid gossip, with West Ham's recent trip to Dublin the latest such shindig to come under the microscope.
Last year Redknapp cancelled Tottenham's Christmas party, but he is not understood to have been involved in his new club's decision.
"No more Christmas parties. We are too busy playing football, we have too many games and they have to concentrate on playing and getting on with their football," Redknapp said in 2011.