Palace have held firm in the past, insisting Zaha would only go for a record fee.
The club want to get the maximum for their talisman as they knew Manchester United would be owed a percentage of the sale through a buy back clause.
But The Mirror reports the 27-year-old is now on the market.
Palace still want a big fee, but will be more flexible, with Everton thought to have a serious interest in the player.
Spurs have also had an interest in the Ivory Coast international in the past, although it is unclear if they could afford a transfer.
Zaha had a poor season and Palace want to grant his wish of playing for a Champions League or Europa League club.