The 22-year-old Colombian striker's switch from Estudiantes has been held up by an issue over his work permit.
"It's whether we think we can get the work permit through, that's the only thing," Allardyce is quoted as saying by Sky Sports News.
"Based on the fact that he's not a full international, we would have to go to a hearing.
"We'd have to decide in the next 24 hours whether - on our part or the player's part - that would be worth doing."
Zapata has made five appearances for Colombia's Under-21 side.