Spurs have been heavily linked with a move for Zaha, with the Mirror reporting back in May that the London club are keen to sign him.
The report adds that Zaha has turned down a contract offer worth in the region of £125k-per-week to stay at Palace. However, the Eagles are set to return with an improved offer for the winger.
Zaha has rediscovered his form after returning to Palace, and enjoyed a fantastic 2017-18 campaign where he scored 12 goals in 29 games for the club.
The north London club are leading the race to sign Zaha, but Palace have put a £70 million price tag on him in a bid to stave off interest.
The Eagles are reportedly looking to offer him an improved £135,000-a-week deal in an attempt to ensure he stays with them.