Zaha was the subject of intense transfer speculation last summer but ended the rumours by signing a new £130,000-a-week deal with the south London club.
The 26-year-old has once again been a standout performer for the Eagles this season, netting eight goals and adding three assists in 30 league matches.
And Palace’s Premier League future for next season is all-but confirmed as they sit eight points clear of the relegation zone with four games left to play.
However, the Ivory Coast international has now set his sights on a move, insisting he wants to fulfil his dream of playing in the Champions League.
Speaking to the Mail, he said: “I’m too ambitious. And not just ambitious to play for a top club, but to win things at club level and with the Ivory Coast.