And they are not put off by his £80m asking price – despite it being way over their whole summer transfer budget.
Starsport revealed how Palace issued a hands-off warning over Zaha this week, insisting he is off the market.
After agreeing to sell Aaron Wan-Bissaka to Manchester United for £50m, they are determined to keep hold of their star man.
But the Ivory Coast star wants out of Selhurst Park and intermediaries have made it clear to Arsenal he wants to join them.
“Arsenal news Crystal Palace Wilfried Zaha transfer latest”
Arsenal news Crystal Palace Wilfried Zaha transfer latest
Zaha was a boyhood Gunners fan and is attracted by the possibility of playing for Unai Emery’s men.
The 26-year-old told Palace earlier this year he wanted to join a club who could offer him Champions League football.
Arsenal failed to qualify after losing to Chelsea in the Europa League final but this has not put Zaha off.
And the Gunners believe Palace will be forced to accept a much lower valuation of the player because he wants to join them.
Any move for Zaha depends on Arsenal being able to sell players – but there is growing confidence they will be successful with a summer clear-out.
Arsenal have so far found it hard to shift high earners like Mesut Ozil and Henrikh Mkhitaryan.
But Laurent Koscielny, Nacho Monreal and Calum Chambers are all among those likely to leave.
Arsenal are also listening to offers for Shkodran Mustafi, with Fenerbahce interested, while Lucas Torreira is wanted by AC Milan.
The Gunners do not want to lose Torreira, or star striker Pierre-Emerick Aubameyang, who was the subject of interest from China.
But there is an acceptance every player has a price, and with Arsenal also pursuing Celtic’s Kieran Tierney and St Etienne defender William Saliba, something has to give.
Arsenal could even offer Palace a player in part exchange for Zaha – but it is understood he is not currently considering making a transfer request to force his way out.