Reports last week claimed manager Unai Emery wanted to break the bank to bring the Ivory Coast international to the Emirates.
Palace want at least £80m for their star player, which is almost double the amount Emery has to spend for the entire summer.
25 per cent of any fee would be given to Zaha's former club, Manchester United.
However, the Gunners' pursuit of Zaha could be helped by the man himself.
The Sun says the 26-year-old continues to harbour dreams of playing for the North London club he supported as a boy.