Allardyce told his club's official website: "The situation with Stelios is an extremely delicate and one that needs to be resolved as quickly as possible.
"If he ends up leaving the Club, which I hope will not happen, we need to find a ready replacement immediately. In the current climate that is going to be a difficult task.
"I very much doubt that there are players out there with the same quality as Stelios, but I hope we don't get to that situation."
Meanwhile, reports from Italy suggest Croatian defender Igor Tudor is on his way to the Reebok.
Juve director general Luciano Moggi revealed: "For Tudor I have an agreement with the English club, Bolton Wanderers.
"But the player prefers the offer he has from Villarreal.
"Personally, I believe he will eventually join Bolton."