Parish revealed Spurs had tabled their opening offer on Thursday but that Palace had immediately knocked back the approach.
“We had a bid from Spurs but £12m – it’s ridiculous. I can’t imagine that they’re serious,” Parish told TalkSport.
“There’s no chance whatsoever of Wilfried Zaha leaving the club in this transfer window. I can absolutely reassure every Palace fan he is an integral part of our plans.
“We’ve told Spurs that there is really no point bidding for him because he is going nowhere – 100 per cent guaranteed.”
Press Association Sport understands Zaha arranged a meeting with manager Alan Pardew at the club’s training ground on Thursday morning where he made clear his wish to join Tottenham.
Zaha is understood to be desperate to leave, with the 23-year-old eager to play under Mauricio Pochettino and test himself in the Champions League.
“It’s not right really that players get their heads turned,” Parish said. “I was told that the manager there thinks he’s the next Ronaldo. Well I’d like to get the next Ronaldo for £12m.
“We need to convince Wilfried that Palace is the right place for him and that he can succeed here.”
Parish added: “I haven’t spoken to the player. The manager and the player might have had a conversation but I’m chairman of the football club.
“I decide who leaves and he’s not leaving. He’ll have to get his head around that.”
Tottenham are keen to add another attacking midfielder to their ranks before the transfer window closes and Zaha, with his youth, energy and athleticism, chimes with the club’s transfer policy since Pochettino took charge.
Zaha was bought by Manchester United in January 2013 but Sir Alex Ferguson, who enjoys a close relationship with Pochettino, had retired by the time the forward arrived the following season.
After failing to establish himself under David Moyes at Old Trafford, Zaha eventually moved back to Palace, initially on loan, and then permanently in February 2015.
Spurs remain in talks with Marseille regarding an £11million transfer for Georges-Kevin Nkoudou and it is understood their pursuit of the winger will not be affected by their interest in Zaha.
Pochettino is wary of being left short by a number of departures, with Clinton Njie set to join Marseille on loan as part of the Nkoudou deal, while Nabil Bentaleb and DeAndre Yedlin have moved to Schalke and Newcastle respectively.
Wolfsburg have also expressed an interest in signing Son Heung-min but Tottenham are not keen to sell the forward, who only moved to White Hart Lane from Bayer Leverkusen 12 months ago.