According to The Sun, Zaha has told Palace that he wants to leave this summer.
The Eagles are willing to listen to offers for the former Manchester United winger, but the London club want as much as 70 pounds as transfer fee for the 27-year-old, according to the report.
This has reportedly led to the Ivory Coast international winger being worried that he will be priced out of the summer transfer market.
Zaha started his professional club football career at Palace and earned the big move to United in 2013.
However, the Ivorian winger failed to make a huge impact at Old Trafford, and after a loan spell back at Selhurst Park in 2014-15, he made a permanent move to the Eagles in 2015.
Zaha scored four goals and provided three assists in the Premier League for Palace this past season, while during the 2018-19 campaign, the winger scored 10 goals and provided five assists in the league for the Eagles.