The 26-year-old Zaha has seen his star rise in recent years in a second stint with the London club after struggling initially with Manchester United.
Zaha earned a name for himself with Palace in the Championship, but managed only one partial season with United, spending part of it on loan at Cardiff, before heading back to Palace.
Following loan and then a £10 million move from Old Trafford back to Selhurst Park, Zaha has blossomed into a Premier League star, scoring 23 goals and 14 assists over the past three seasons in the English top-flight.
Palace warded off interest last summer by making Zaha the highest paid player at the club on a contract that runs through 2023.
However, after another strong season, the Ivory Coast attacker seems intent securing another opportunity to play for a Champions League club in the near future.
“I'm too ambitious,” Zaha told the Daily Mail. “And not ambitious just to play for a top club, but to win things at club level and with the Ivory Coast.
“For me to be better, to achieve what I know I am capable of, I have to aim to play at the very highest level, to win trophies.”
Zaha does feel grateful to have achieved what he has thus far in his career, but believes he can prove himself on the greatest of stages if given the opportunity.
“I'm blessed to have come this far in my playing career. But I feel like there is so much more I have to offer.
“I have to experience the Champions League. I just need the opportunity, that's it. And I'll do the rest.”
Crystal Palace have four games remaining in the season, and are likely safe from relegation but can play some role in deciding the top four as they visit Arsenal on Sunday.
In addition to club play, Zaha can work toward achieving his dreams on the international stage this summer when Ivory Coast compete in the Africa Cup of Nations this summer.