The England U21 international has been watched extensively by Premier League scouts during a season in which he has been the outstanding player in the Championship.
Gunners boss Arsene Wenger is determined to add to his attacking options in the forthcoming transfer window, and has identified Zaha as the man he wants to bring to the Emirates Stadium.
However, with Palace pushing for promotion this year, they are unlikely to sell midway through the season, unless an exceptional offer is received.
Arsenal's track record of giving young players regular first-team football could work in their favour in the chase for Zaha, who will garner a fee in the region of £18million.
Eagles boss Ian Holloway will be determined to keep the talented youngster at Selhurst Park, but with a number of clubs planning January bids, they are facing a battle to retain his signature.