The newspaper claims Zaha "might want to try himself at a 'big club' again" after a spell with Manchester United earlier in his career.
It adds, however, that Palace are set to return with an improved offer for the winger they allegedly value at £70 million, and could go to £135,000 a week after removing Yohan Cabaye from the wage bill.
Tottenham have long been credited with interest in Zaha and are leading the race for his signature, according to the Sun, although it remains to be seen whether they - not to mention Everton or Dortmund - could afford the Crystal Palace academy product.
Tottenham's wide options include Erik Lamela, Lucas Moura and Georges-Kevin N'Koudou, with Theo Walcott, Ademola Lookman, Nikola Vlasic and Yannick Bolasie, the former Crystal Palace player, all capable of playing there for Everton.
Could Zaha quit Crystal Palace for Tottenham Hotspur, Everton or Borussia Dortmund this summer?