The Ivory Coast international has enjoyed his most productive Premier League season yet, contributing directly to 16 goals and seeing his name linked with a move to Tottenham Hotspur and Arsenal.
Allardyce is not concerned about the ongoing speculation, however, as he expects Zaha to commit his future to the club in the coming weeks once an agreement can be struck.
"I think it is in negotiation, but I don't know how far it's gone and I certainly don't know what the figures are," he told reporters. "The figures that have been bandied about in the papers I would have thought they have been hugely exaggerated as they are always because it probably came from the agent.
"He loves Palace. As a youngster he has been brought up here, had a brief spell at Manchester United, came back, flourishing, getting a lot of publicity and, of course, with a bigger contract there is a bigger responsibility.
"So when he gets the bigger contract I will be expecting a lot more than I am already getting which is saying something because I am getting an awful lot now."
Zaha returns to former side Manchester United on the final day of the season, where he made just two league appearances - both from the bench - during a disappointing stint at the club in 2013-14.