Gerard Pique is poised to miss around three months out with his knee injury. The club wouldn't be allowed an emergency signing even if it was five months plus, as the rule was taken out in the summer. So Barcelona will be left short at the back until January, with currently only Clement Lenglet fit at centre back.
Furthermore, if the Catalans decide to sign a player in January (Eric Garcia, for example), there are other issues. They currently have 24 of 25 places filled in the squad - that's the maximum allowed in La Liga. They also have Ansu Fati out injured long term and want a forward to replace him, so they will on;y be able to get one, unless they can let another player go.
Money is also a problem; they don't have any.
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Another option exists, an unlikely one, which would be unregistering Pique if they think his knee injury is serious enough to make it feasible.