The winger, 24, has produced the best football of his career to inspire Palace's recent resurgence as they battle against relegation.
Allardyce has already instructed Zaha to strive to reach the level at which Eden Hazard regularly plays, while Palace chairman Steve Parish has spoken of plans to offer him a new contract once their Premier League status is secured.
Zaha has long been a reported transfer target for Tottenham, and ahead of Wednesday evening's fixture at Southampton his manager has reminded him of where his priorities should lie.
"Hopefully Wilf is not listening to all that the papers are saying, good or bad, and it doesn't distract him from the performances he is giving," Allardyce said. "You can get distracted by good publicity as well as bad, and he has to consistently perform to the level he is at and that gives him a greater value, and Steve has chosen maybe to offer a new deal.
"Whether Wilf accepts that, maybe on the basis that he likes this club and what the club's done for him, only time will tell. So come the end of the season, make sure we are in the Premier League and those talks can take place, but until then shut up about it.
"He's maturing as a person and that maturity is producing consistent performances. I don't want him to get distracted from the focus, which is getting better and keeping us in the Premier League.
Read the full article on eurosport.co.uk: Allardyce urges Zaha to focus on Crystal Palace amid transfer rumours