The Gunners had a £40m bid rejected by the club for the forward with Palace said to be holding out for something closer to £80m.
Palace face a battle to keep hold of their talisman after he revealed at the end of last season that he wants to play in European competitions.
Zaha’s brother also put pressure on the club by revealing it is the Palace academy players’ dream to play for Arsenal.
Following Palace’s 6-2 defeat against Barnet, Roy Hodgson revealed the clubs are still some way apart in their valuation of the forward.
Transfer verdict 2019: Stay or go?
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“I don't think Arsenal have actually made a bid that has come anywhere near our valuation,” the Palace manager told Sky Sports.
“I'm sure the player realises that if someone's going to take him away from us, he'll expect clubs to pay the market value.
“Until someone does that, there's not much to discuss regarding Wilf.”
Arsenal are very keen to sign Wilfried Zaha
(The Independent)
Arsenal were also handed a blow to their chances of signing Kieran Tierney from Celtic when boss Neil Lennon said the Scottish champions will not let go of the left-back for a cheap price.
Lennon pointed to the £50m that United spent to sign 21-year-old Aaron Wan-Bissaka from Palace as a mark of where the current market is.
Celtic rejected Arsenal’s second offer in the region of £25m for the Celtic defender and Lennon said the club are in a strong position. "The club's valuation of Kieran has not been met and until then we don't have a discussion."
Unai Emery is desperate to add to his playing squad and provided some positive news on Arsenal’s pursuit of Real Madrid midfielder Dani Ceballos. “I don’t want to speak about the names but Ceballos is a very good player,” he said.
"We are being very, very demanding and we are first speaking about the possibility to sign very big, very expensive players."
Arsenal are in a difficult position this transfer window after Josh Kronke admitted the club were working with a “Europa League transfer budget with a Champions League wage budget.”
Everton Soares remains a target if the club fail to bring Zaha to The Emirates and an Arsenal medic was sent to monitor the Gremio forward.
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