Tottenham reportedly bid £14m for Zaha during the summer but Palace chairman Steve Parish said cashing in on the 24-year-old would have been "a bridge too far for the club," having already sold Yannick Bolasie to Everton during that transfer window.
Having remained in South-east London, Zaha has enjoyed his best campaign in the Premier League to date, having scored three goals and provided eight assists in 17 appearances.
Palace are now set lose the former Manchester United winger for up to a month after he was named in the Ivory Coast squad for the 2017 Africa Cup of Nations, which kicks off on the 14 January. But while he is away, Palace will resist any improved offers for their star player, despite reports from the Guardian suggesting Tottenham could return with a £30m offer.
"I knew before I got here that he [Zaha] was going to the African Nations and good luck to him," Allarydce told a press conference ahead of Palace's trip to Arsenal on Sunday (1 January).
"It is fantastic for him but obviously a big loss for us. But there is no chance of losing him permanently, according to the chairman."
Allardyce marked his return to the Premier League with a point away to Watford on Boxing Day and is now eager to strengthen his squad, with the Eagles sat just two points off the relegation zone. The former England manager appeared to confirm reports he is looking to sign Arsenal full-back Carl Jenkinson on loan but is unsure if the Gunners will allow the full-back to leave.
"Certainly the chairman would like to sign a couple if possible, but finding two is hard enough and with today's inflated prices you have to be certain they will work for you and make the team better.
"We've got one loan left and we would look at what is available. I don't know whether he (Jenkinson) is yet."