"The emergence of a top-line player in the transfer window, under our budget restrictions, is unlikely," Allardyce revealed.
"To pull out a signing like Vincent Candela, to magic up someone like him, as I did last year, is highly unlikely.
"We might have to wait until 10.30pm on January 31 and hope one pops out of the hat."
Meanwhile, Sam Allardyce has also played down talk of Champions League qualification this season.
"I don't know about the Champions League," he said after Saturday's win over Manchester City. "I am just happy winning this game with the few players I've got. They are covering up for our shortage of players.
"It was a tremendous performance and a tremendous effort from the players.
"That's our 12th clean sheet of the season - the best we have ever done. If we keep in that mode at home it is going to bring us a lot of success."