The Sun understand the 25-year-old wants to play for a big club again and has turned down the Eagles latest offer as a result.
News of Zahas desire to leave Selhurst Park will pique the interest of long-term suitors Tottenham, who have previously had bids for the Ivory Coast international turned down.
But Palace have slapped a £70m price tag on Zaha to warn off any interested parties but it remains to be seen whether that will be enough.
Zaha played a pivotal role in Palace beating the drop last season, scoring nine goals and contributing five assists as Roy Hodgsons side survived dropping into the Championship.
Tottenham are yet to make a single signing this summer, while their rivals Arsenal, Liverpool and Manchester United have all made additions to their respective squads.
They have previously had two bids turned down for Zaha, both of which came last summer, and decided against a January move for the ex-United winger.
But reports in February surfaced claiming Tottenham would reignite their interest this summer – and the news that a fresh contract has been turned down will only encourage that pursuit.
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In May 2017, Zaha signed a new five-year contract to commit his future to Palace but his improvement last season following his return from a second knee problem has increased his value.
Goals against Bournemouth, Brighton and Hove Albion, Leicester City and then on the final day against West Bromwich Albion proved key in Palace staying in the Premier League, as Hodgsons side secured an 11th place finish.
Yohan Cabaye earlier this summer turned down a new deal with Palace and has joined Al Nasr after three seasons with the club.