The Ivory Coast international, who previously endured a tough two-year spell with Manchester United, has proven his quality with Palace over recent seasons.
The 24-year-old helped keep the Eagles in the Premier League last term and has again been influential in 2017-18.
Zaha missed the early stages of the campaign through injury but he has been influential since his return, netting in the win over Chelsea, while he also scored a late equaliser against West Ham.
Reports claim that Arsene Wenger is a big admirer of the winger and hopes Zaha can replace Alexzis Sanchez, who is expected to depart at the end of the term.
Palace only recently handed Zaha a new contract amid interest from Tottenham and it's understood that they will demand a fee in the region of £35million.