Owen Coyle’s side had a bid of £4 million rejected for the young winger on Monday, and were expected to increase the figure to £7m today in a bid to prise the starlet from Selhurst Park.
Parish has poured scorn on Bolton’s bid for Zaha - a player who is widely regarded as one of the finest talents outside the Premier League – and insisited he will not be sold before the window slams shut.
He told the London Evening Standard: "We have had a bid from Bolton that isn't worth talking about and no one is going anywhere.
"I think that after the financial problems the club has been in previously, many people seem to think they can kick us in the nuts.
"As for the figure of £7m - I don't know where they got that from. I'm very happy, though. No one has given us a decision to make so it's where we want to be."
Young full-back Nathaniel Clyne has also been linked with a move away from the Championship side in recent weeks, with Manchester United one of several mooted destinations.
Despite uncertainty surrounding a new contract, Parish made it clear that Clyne will likewise be staying with the club, adding: "He will still be here and we will see what happens [with his contract] after that.”