Unai Emery’s side have already seen their opening bid of £40m turned down by Palace, who are demanding £80m for their star attacker.
The Gunners are restricted this summer with a £45m budget and Zaha’s valuation is well beyond their price range.
But according to The Sun, Arsenal have attempted to bridge the gap by offering £40m plus Mohamed Elneny, Calum Chambers and Carl Jenkinson to Palace.
The report claims that Arsenal value the three players at £40m and will remind Palace that the offer would reduce the sell-on fee owed to Manchester United.
United are entitled to 25 per cent of Zaha’s transfer fee as Palace failed to remove the clause during their negotiations for Aaron Wan-Bissaka.