But the Eagles’ £80million asking price could end the Gunners’ pursuit.
It has been claimed that Zaha has told Palace chiefs he wants to leave for a Champions League club this summer.
And Arsenal will qualify for next season’s competition if they beat Chelsea in the Europa League final on May 29.
The Sun claim Unai Emery’s transfer budget will be around £40million if they fail to make the Champions League and he is keen to bring Zaha to the Emirates.
The Gunners could offer Callum Chambers, Carl Jenkinson or Reiss Nelson as part of any potential deal for the Ivory Coast international.
Zaha became the Eagles’ top earner on a reported £130,000-a-week deal after signing a new five-year contract last August.
It has put Palace chairman Steve Parish in a position to demand big money for his star man, who scored ten goals in the 2018/19 Premier League season.
Last month, Zaha said he wanted the opportunity to play in the Champions League.
He told the Daily Mail: “I’m too ambitious. And not ambitious just to play for a top club, but to win things at club level and with the Ivory Coast.