Zaha's agent told BBC Sport on Thursday that Spurs had bid £15m for the 23-year-old England international.
Pardew is keen to keep the former Manchester United player and said Parish had "made his position clear".
"He was our player of the year and is a fans' favourite," Pardew said of Zaha, who scored five goals last season.
"Wilf came and saw me, he believed there was interest from Tottenham. I don't even know what the bid is. The chairman has made his position clear and I stand by that. That's the right thing for us."
Zaha, who rejoined Palace in February 2015 for £3m just two years after a £15m move to Old Trafford, made the first of his two England appearances in 2012 but has not been picked since 2013.
Crystal Palace chairman Steve Parish "put the full stop" on Tottenham's interest in winger Wilfried Zaha, according to Eagles boss Alan Pardew.