Zaha’s current deal expires next summer and he is free to talk to overseas clubs in January.
The winger has been verbally offered a pay rise to his £130,000-a-week deal, though he is yet to receive a written offer and is not close to agreeing an extension.
That has raised concerns he could seek a Palace exit.
Arsenal came close to signing Zaha in 2019 before they instead bought Nicolas Pepe.
Chelsea were also interested in the Ivory Coast international last summer but instead opted to sign Pierre-Emerick Aubameyang as they needed a No9.
The Blues may revive their interest but have a pre-contract agreement to sign Christopher Nkunku from RB Leipzig for around £50m and he is a similar profile of player to Zaha.
At Palace, Zaha is enjoying one of his best seasons and already has six goals and one assist in 11 appearances under Patrick Vieira.